{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Julia\n",
    "\n",
    "### Many thanks to Diego Castañeda for writing much of the code in this notebook.\n",
    "\n",
    "As languages go, [installing Julia](http://julialang.org/downloads/platform.html) is a piece of cake. You also need [IJulia](https://github.com/JuliaLang/IJulia.jl) to run this notebook. You will also need to instal the PyPlot package, ToeplitzMatrices and MultivariateStats:\n",
    "\n",
    "    Pkg.add(\"PyPlot\")\n",
    "    Pkg.add(\"MultivariateStats\")\n",
    "    Pkg.clone(\"https://github.com/JuliaMatrices/ToeplitzMatrices.jl.git\")\n",
    "\n",
    "I'm using Julia v0.5. \n",
    "\n",
    "## Some preliminary functions\n",
    "\n",
    "[Basic array help.](http://docs.julialang.org/en/release-0.5/manual/arrays/)\n",
    "\n",
    "[The linalg help is here.](http://docs.julialang.org/en/release-0.5/stdlib/linalg/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "misfit (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function norm(m)\n",
    "    return m' * m\n",
    "end\n",
    "\n",
    "function misfit(d, d_pred)\n",
    "    misfit = (d_pred .- d)' * (d_pred .- d)\n",
    "    return misfit[1]\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "plot_all (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function plot_all(m, d, m_est, d_pred)\n",
    "    #=\n",
    "    Helper function for plotting. You can ignore this.\n",
    "    =#\n",
    "    \n",
    "    fig = figure(figsize=(10,6))\n",
    "\n",
    "    ax0 = fig[:add_subplot](2,2,1)\n",
    "    ax0[:plot](m)\n",
    "    t = L\"$\\mathrm{Model}$\"\n",
    "    ax0[:set_title](t)\n",
    "    ax0_mi, ax0_ma = ax0[:get_ylim]()\n",
    "\n",
    "    ax1 = fig[:add_subplot](2,2,2)\n",
    "    ax1[:plot](d, \"o\", mew=0)\n",
    "    ax1[:set_title](L\"$\\mathrm{Data}\\ d$\")\n",
    "    ax1_mi, ax1_ma = ax1[:get_ylim]()\n",
    "    \n",
    "    ax2 = fig[:add_subplot](2,2,3)\n",
    "    ax2[:plot](m, alpha=0.25)\n",
    "    ax2[:plot](m_est)\n",
    "    t = L\"$\\mathrm{Estimated\\, model}$\"\n",
    "    ax2[:set_title](t)\n",
    "    ax2_mi, ax2_ma = ax2[:get_ylim]()\n",
    "    \n",
    "    ax3 = fig[:add_subplot](2,2,4)\n",
    "    ax3[:plot](d, \"o\", mew=0, alpha=0.25)\n",
    "    ax3[:plot](d_pred, \"o\", mew=0)\n",
    "    t = L\"$\\mathrm{{Predicted\\ data}}$\"\n",
    "    ax3[:set_title](t)\n",
    "    ax3_mi, ax3_ma = ax3[:get_ylim]()\n",
    "    \n",
    "    show()\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can add a user made library to generate Toeplitz matrices: Pkg.clone(\"https://github.com/JuliaMatrices/ToeplitzMatrices.jl.git\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "convmtx (generic function with 1 method)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "using ToeplitzMatrices\n",
    "function convmtx(h, n)\n",
    "    #=\n",
    "    Equivalent of MATLAB's convmtx function, http://www.mathworks.com/help/signal/ref/convmtx.html.\n",
    "    \n",
    "    Makes the convolution matrix, C. The product C.x is the convolution of h and x.\n",
    "    \n",
    "    Args\n",
    "        h (ndarray): a 1D array, the kernel.\n",
    "        n (int): the number of rows to make.\n",
    "        \n",
    "    Returns\n",
    "        ndarray. Size m+n-1\n",
    "    =#\n",
    "    col_1 = append!([h[1]],zeros(n-1))\n",
    "    row_1 = append!(h,zeros(n-1))\n",
    "    return Toeplitz(col_1, row_1)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition ricker() in module Main at In[5]:5 overwritten at In[13]:5.\n",
      "WARNING: Method definition ricker(Any) in module Main at In[5]:5 overwritten at In[13]:5.\n",
      "WARNING: Method definition ricker(Any, Any) in module Main at In[5]:5 overwritten at In[13]:5.\n",
      "WARNING: Method definition ricker(Any, Any, Any) in module Main at In[5]:5 overwritten at In[13]:5.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "ricker (generic function with 4 methods)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Implements bruges's ricker.\n",
    "function ricker(f=25, length=0.128, dt=0.001)\n",
    "\n",
    "    # Time basis.\n",
    "    t = collect(0:dt:length) .- length/2\n",
    "    \n",
    "    # Amplitudes.\n",
    "    x = 1 - 2 * pi^2 * f^2 .* t.^2\n",
    "    y = exp(-pi^2 * f^2 .* t.^2)\n",
    "    a = x .* y\n",
    "\n",
    "    return t, a\n",
    "end"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8400000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = 50\n",
    "\n",
    "#                    VP    RHO\n",
    "m_ = ones((M, 1)) * 2550 * 2650  \n",
    "m_[11:15,:] =       2700 * 2750   \n",
    "m_[16:27,:] =       2400 * 2450\n",
    "m_[28:35,:] =       2800 * 3000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mhjt37iA2NhYAkJeXB4VCgRMnTmDHjh3w8/PD+vXr+d12bm5uVtdbpvxMJhNcXFxgMpn4aT5b2u4790wmU485iYjX9tV+f3N2z9XfMTEYIwlmSIzhhl2GtH37dtTU1ODrr7/m7wyWLl2Kjo4OvPLKK0hOToZUKgUAtLa2Wl3f0tICALxGKpWira3NZlstLS28zqLtKadIJBLk7K39/uZ8sJ/9HVNvbNq0CV5eXoJYcnIykpOT+7yWwRhoLLPMI20NidVEGnoKCgpQUFAgiN2/f3/A27HLkM6ePYsZM2ZYTV3Fx8fj/fffR1lZGb8eY5m6605dXR0UCgVcXFwAdE13dXR0wGAwCKbtzGYz7t27B39/fz6mVqt7zAmA16rVahBRj9oHc54+fbrPnAqFAm5ubv1qvzdycnJsroMxGI6gsRFwcQF6mKQYtigUgMnU9dWP3wMZA4CtX5x1Op3VWv2jYtcaktlsRkdHh804EaG9vR3+/v7w8fFBaWmple7SpUsIDw/nfw4PDwcRWWkvX76Mzs5OK61Op7PKeeHCBbi7uyMkJAQAMG3aNIjFYqucZrMZer3eKmdzczMqKiqscopEIl4rEokQFhZmc0wXL15EUFCQYEcfgzESGGkHq1qwHB/0/feO7Qdj4LHLkGbMmIGysjLcvHlTED948CDGjBmDxx9/HADwzDPP4MMPP0RNTQ2v+fTTT1FZWSl42DQ6OhoKhQK7d+8W5Nu9ezdkMhni4uL4WGJiIm7fvo2ioiI+ZjAYcOTIEcTHx/N3XZ6enli8eDH2798v2Pm2b98+NDU1CdpPSEiAWCyGVqsVtJ+bm4uAgADMnTtX0P7ly5cFpnjjxg2cPHlSkJPBGCmMdEO6d8+x/WAMAvY8tPTFF1+QVColX19feu2110ir1VJsbCxxHEfr1q3jdbdu3SIfHx+aNGkSvf322/T666+TQqGg8PBwamtrE+TUarXEcRwlJSVRXl4epaSkEMdxlJmZKdB1dHTQnDlzyNPTk7Zv305arZamTZtGXl5eVFlZKdDqdDqSSqU0c+ZMys3NpYyMDJJKpRQbG2s1pvT0dL7/eXl5FBcXRxzHUWFhoUBnNBpp0qRJ5OvrS9nZ2ZSTk0OBgYE0fvx4MhgMvb5v7MFYxnBk0yaiqVMd3Qv7uXGj64He06cd3ZPRzWB8rtllSEREly5dotjYWPLy8iI3NzeaMmUKZWZmUkdHh0B3/fp1iomJIblcTgqFglJSUujOnTs2c+bl5dHUqVNJIpFQcHAw7dq1y6auoaGB1qxZQz4+PiSXyyk6Opp0Op1N7dmzZ2n+/Pnk7u5Ovr6+lJaWJji5oTuZmZk0YcIEkkgkFBYWRgUFBTZ1NTU1pNFoaOzYseTp6UkJCQlUVVXV01vFwwyJMRxZu5Zo1ixH98J+7t7tMqRuh7YwHMBgfK6JiFh1+sHGsvh35coVtqmBMWxYuRKoqwNOnnR0T+yjvb1rM0ZeHvDii47uzehlMD7XWPkJBmOUMtJqIVkQiwEvL7b12xlhhsRgjFJG6qYGgD2L5KwwQ2IwRikj2ZDYaQ3OCTMkBmOUwgyJMdxghsRgjFJGWvny7igU7DkkZ4QZEoMxShmpmxoAdofkrDBDYjBGKWzKjjHcYIbEYIxCzGagtZUZEmN4wQyJwRiFWI55HMmG1NTUZaoM54EZEoMxChnphqRUdn1nJ347F8yQGIxRiKVa7Eje1ACwaTtngxkSgzEKGanlyy0wQ3JO7DKk559/HhzH9fhlqZ763HPP2Xw9NDTUZt78/HyEhoZCKpUiJCQE77zzjk3d/fv3sXbtWowbNw5yuRzR0dEoKyuzqT137hzmz58PmUwGtVqNjRs3CuojWSAivPHGGwgKCoJUKsX06dNRWFhoM2dtbS00Gg28vb3h5eWFpUuX4ptvvunPW8dgDCuYITGGI3aVMP/lL3+Jn//854IYEWHdunUICgriS5uLRCJIJBLk5+ej+2HiXl5eVjn37NmD1NRUJCUlYfPmzfj888+RlpYGk8mELVu2CNpZsmQJysvLkZ6eDqVSCa1Wi6ioKOh0OkycOJHX6vV6LF68GKGhocjJyUF1dTWys7Nx8+ZNnDhxQtD+1q1bkZWVhXXr1iEyMhLFxcVYsWIFOI4TFN5rampCVFQUjEYjtm3bBrFYjJ07dyIqKgp6vR7e3t72vJUMhkMZ6YZk+e/GHo51Mh61fsWZM2dIJBIJCuo999xz5OHh0ee1JpOJVCoVxcfHC+KrVq0iDw8Pamho4GOHDh0ikUhERd2KoNy9e5e8vb1p5cqVgutjY2MpICBAUP8oLy+POI6jTz75hI/V1NSQq6srpaWlCa5fuHAhBQYGUmdnJx/LysoijuMEtT8qKipILBZTRkZGr+Nk9ZAYw41Dh7pqCv3wg6N78vB4eBC9+aajezF6GYzPtUdeQzpw4AA4jkNycrLVa52dnTAajT1ee+rUKdTX12P9+vWC+EsvvYTGxkbB3czRo0fh5+eHZcuW8TGVSgWNRoPi4mKYzWYAgNFoRElJCVavXg1ZtxXblJQUyGQyHD58mI8dP34c7e3tSE1NFbSfmpqK6upqnD9/XtD+rFmzBHU/Jk+ejEWLFglyMhgjAcsdkru7Y/vxKLBnkZyPRzKk9vZ2/OlPf8K8efMQGBgoeK25uRmenp7w8vKCUqnEhg0brNZwLOs/ERERgnhERAQ4jhOsD5WVldksAjV79mw0NzejsrISAFBeXo729narnC4uLggPDxfk1Ov1kMlkmDJlilVOIuK1RISrV68iMjLSZvtVVVU216cYjOFKYyMglQJjxji6Jw8PMyTn45EM6eOPP8a9e/ewcuVKQdzf3x/p6el47733UFhYiISEBGi1WsTGxqKzs5PX1dXVYcyYMVCpVILrXVxcoFQqUVtbK9Ba1qi6Y4lZtHV1dRCJRD1qH8zp6+vbZ876+nq0trb2q30GYyQwko8NssBqIjkfdm1qeJCDBw/C1dUVSUlJgviOHTsEP2s0GgQHB2Pbtm04cuQIv1nAZDLB1dXVZm6JRAKTycT/bDKZ4ObmZlNHRLzW8r0nbX9zds/VV87uGgZjJOAMhsTukJyPh75DampqwgcffICYmJh+7TDbtGkTRCIRSkpK+JhUKkVbW5tNfUtLC6RSqUDbauOckJaWFohEIl5r+d6Ttr85u+fqK2d3DYMxEhjJpScsMENyPh76DunYsWMwmUxW03U9IZFIoFQqUd/tX5BarUZHRwcMBoNg2s5sNuPevXvw9/cXaC3POXXHErNo1Wo1iKhH7YM5T58+3WdOhUIBNze3frXfG5s2bbLa+p6cnGxzQwiDMZiM5NITFpghDR0FBQUoKCgQxO7fvz/g7Ty0IR04cAByuRxPPfVUv/SNjY0wGAzw8fHhY+Hh4SAilJaWIiYmho9fvnwZnZ2dCA8PF2jPnDljlffChQtwd3dHSEgIAGDatGkQi8UoLS1FYmIirzObzdDr9Vi+fLkgZ35+PioqKgQbGy5cuACRSMS3LxKJEBYWhtLSUqv2L168iKCgIMGOvp7IycmxuTGDwRhqnGXKjj2HNDTY+sVZp9NZbR57VB5qys5gMODTTz/F008/za+hWGhtbUWjZU9pN7Zv3w4AiI2N5WPR0dFQKBTYvXu3QLt7927IZDLExcXxscTERNy+fRtFRUWCfhw5cgTx8fFwcXEBAHh6emLx4sXYv3+/YOfbvn370NTUJHjYNSEhAWKxGFqtVtB+bm4uAgICMHfuXEH7ly9fhk6n42M3btzAyZMnBTkZjJGAsxiS0dhVSoPhHDzUHVJhYSE6OjpsTtf9/e9/x4wZM5CcnMzfdXz88cf46KOPsGTJEsTHx/NaiUSC1157DRs2bIBGo8ETTzyBv/71rzh48CBef/11jB07ltcmJibij3/8I55//nl8+eWXUKlU0Gq16OzsxH/8x38I+rBjxw7MmzcPCxcuxNq1a3Hr1i3s3LkTTzzxhOCkiYCAALz88st488030dbWhlmzZuHYsWM4e/YsDh48CJFIxGvXr1+PvXv3YsmSJfjNb34DsViMnJwcqNVq/PrXv36Yt9Hp2bABOHRocNsYMwb47/8GHjhAhNEHjY3AA09qjDgsxwd9/z0wbpxj+8IYGB7KkA4ePAhfX18sWrTI6rWxY8fiqaeeQklJCfbt24eOjg5MmjQJmZmZ2Lx5s5U+NTUVrq6u+MMf/oD/+Z//wfjx4/HHP/4Rv/rVrwQ6juPw0UcfYcuWLXj77bdhMpkwe/Zs7Nu3D8HBwQLtjBkzUFJSgldeeQW//vWv4eHhgTVr1uD111+3aj8rKwsKhQJ79uzB+++/j+DgYBw4cEAwtQcAcrkcn332GTZt2oQdO3ags7MTP/vZz7Bz504oLWfhMwQcPQrMnAlERQ1eG7//PXDpEjMke3GWTQ1A1zoSMyTnQETU7bA5xqBgmWu9cuXKqFlDMhgAH5+uO6TBnNGcOhWIjQV27hy8NpyRKVOAJ58E3nzT0T15eK5fB378Y+DsWaDb7DpjiBiMzzVWfoIxKFy71vU9LGxw21Eq2cL2w+Asa0gA22nnTDBDYgwK5eWAqyswadLgtqNUdt2NMezDGQzJ8vgjMyTngRkSY1C4dq1rOu0fmx8HDZWK3SHZC5FzGJKbW9ezVMyQnAdmSIxBobwcmDZt8NthU3b209YGdHSMfEMC2LNIzgYzJMaAQ9R1hzTY60cAM6SHYaQX5+sOO63BuWCGxBhw/va3rgcWh8KQVKqu51Da2we/LWfBYkgj/egggBmSs8EMiTHglJd3fR+qKTugy5QY/YPdITGGK8yQGAPOtWuApycwfvzgt2UxJDZt13+cyZBYTSTnghkSY8CxbGjodvLSoMEMyX6cyZDYHZJzwQyJMeAM1YYGoGsNCWDPItmD5cxhZkiM4QYzJMaAYjYDX301dIZkeVqf3SH1H2fb1NDQ0LWNnTHyYYbEGFAqK7tMaSg2NACAWAx4eTFDsofGxq7pVGcoctz9xG/GyIcZEmNAsZxhN1SGBLBnkezFckrDUKzxDTbsPDvnwi5Dev7558FxnM2vMWPGCEp8V1RUICYmBh4eHlAqlUhJSYGhh4n+/Px8hIaGQiqVIiQkBO+8845N3f3797F27VqMGzcOcrkc0dHRKCsrs6k9d+4c5s+fD5lMBrVajY0bNwoK9lkgIrzxxhsICgqCVCrF9OnTUVhYaDNnbW0tNBoNvL294eXlhaVLl+Kbb77p620bVZSXA2r1PzcbDAUqFVtDsgdnODbIAjMk58Kueki//OUvBQXugK4P9HXr1iEoKAhqtRoAUFNTgwULFsDb2xuZmZkwGo3Izs7GtWvXcOnSJYjF/2x2z549SE1NRVJSEjZv3ozPP/8caWlpMJlM2LJli6CdJUuWoLy8HOnp6VAqldBqtYiKioJOp8PEiRN5rV6vx+LFixEaGoqcnBxUV1cjOzsbN2/exIkTJwT937p1K7KysrBu3TpERkaiuLgYK1asAMdxgkqwTU1NiIqKgtFoxLZt2yAWi7Fz505ERUVBr9fD23LS4yhnKDc0WGB3SPbhDLWQLDBDcjLoETlz5gyJRCLKzMzkY6mpqSSTyai6upqPlZSUkEgkor179/Ixk8lEKpWK4uPjBTlXrVpFHh4e1NDQwMcOHTpEIpGIioqK+Njdu3fJ29ubVq5cKbg+NjaWAgICqLGxkY/l5eURx3H0ySef8LGamhpydXWltLQ0wfULFy6kwMBA6uzs5GNZWVnEcRxduXKFj1VUVJBYLKaMjIxe36MrV64QAMG1zkpQENHmzUPb5qpVRAsWDG2bI5n164nCwx3di4GhuZkIIPrv/3Z0T0Yfg/G59shrSAcOHADHcUhOTuZjRUVFePLJJxEQEMDHFi1ahJCQEBw+fJiPnTp1CvX19Vi/fr0g50svvYTGxkbB3czRo0fh5+eHZcuW8TGVSgWNRoPi4mKYzWYAgNFoRElJCVavXg1Zt21EKSkpkMlkgvaPHz+O9vZ2pKamCtpPTU084d+KAAAgAElEQVRFdXU1zp8/L2h/1qxZgkJUkydPxqJFiwQ5RzNNTcD//d/Qrh8BrASFvTjTlJ1U2vXF7pCcg0cypPb2dvzpT3/CvHnzEBgYCKBrneXOnTuIjIy00s+ePVuw5mP5c0REhEAXEREBjuOstLaqEs6ePRvNzc2orKwEAJSXl6O9vd0qp4uLC8LDwwU59Xo9ZDIZpkyZYpWTiHgtEeHq1as9jqmqqsrm+tRo48svu74P9ZQdK0FhH85kSAB7FsmZeCRD+vjjj3Hv3j2sXLmSj1k2NljWk7qjVqtRX1/P383U1dVhzJgxUFmebvwHLi4uUCqVqK2tFeTtKScAXltXVweRSNSj9sGcvr6+feasr69Ha2trv9ofzZSXd+3cmjp1aNu1HB9DNLTtjlSYITGGK49kSAcPHoSrqyuSkpL4mMlkAgC4ublZ6SUSiUBjMpng6upqM7dEIuF1Fm1POYlIkLO39vub88F+9ndMo5lr17oqxLq7D227SmXXad8//DC07Y5UnGlTA8BqIjkTdu2y605TUxM++OADxMTECHaYSf/xtF1ra6vVNS0tLQKNVCpFW1ubzfwtLS28zqLtKadIJBLk7K39/uZ8sJ/9HVNvbNq0CV5eXoJYcnKyYP1tJFNePvTTdcA/t5gbDF0PyTJ6p7HROU5psMDukAafgoICFBQUCGL3798f8HYe2pCOHTsGk8kkmK4D/jmF1f2ZJAt1dXVQKBRw+Udda7VajY6ODhgMBsG0ndlsxr179+Dv7y/I21NOALxWrVaDiHrUPpjz9OnTfeZUKBRwc3PrV/u9kZOTY3MdzFm4dg1Yt27o27X807l3D+i2+5/RA844ZWcpecIYHGz94qzT6azW6h+Vh56yO3DgAORyOZ566ilB3N/fHz4+PigtLbW65tKlSwgPD+d/Dg8PBxFZaS9fvozOzk4rrU6ns8p54cIFuLu7IyQkBAAwbdo0iMViq5xmsxl6vd4qZ3NzMyoqKqxyikQiXisSiRAWFmZzTBcvXkRQUJBgR99o5O5d4PZtx94hsWmb/uGMhsTukJyDhzIkg8GATz/9FE8//TS/htKdZ555Bh9++CFqamr42KefforKykrBw6bR0dFQKBTYvXu34Prdu3dDJpMhLi6OjyUmJuL27dsoKioS9OPIkSOIj4/n77o8PT2xePFi7N+/X7Dzbd++fWhqahK0n5CQALFYDK1WK2g/NzcXAQEBmDt3rqD9y5cvC0zxxo0bOHnypCDnaMURRwZZYIZkH85mSKwmkhPxMA8vvf3221YPmXbn1q1b5OPjQ5MmTaK3336bXn/9dVIoFBQeHk5tbW0CrVarJY7jKCkpifLy8iglJYU4jhM8aEtE1NHRQXPmzCFPT0/avn07abVamjZtGnl5eVFlZaVAq9PpSCqV0syZMyk3N5cyMjJIKpVSbGysVV/T09OJ4zhat24d5eXlUVxcHHEcR4WFhQKd0WikSZMmka+vL2VnZ1NOTg4FBgbS+PHjyWAw9Pp+jYYHY996i8jNjchsdkz77u5EOTmOaXsk0dFBJBIRdXs+fcTz7rtdY+rocHRPRheD8bn2UIY0Z84cUqvVgpMMHuT69esUExNDcrmcFAoFpaSk0J07d2xq8/LyaOrUqSSRSCg4OJh27dplU9fQ0EBr1qwhHx8fksvlFB0dTTqdzqb27NmzNH/+fHJ3dydfX19KS0sTnNzQnczMTJowYQJJJBIKCwujgoICm7qamhrSaDQ0duxY8vT0pISEBKqqqurxPbAwGgzp3/6NaMYMx7U/fjzRtm2Oa3+k0NjYdbLBwYOO7snAceRI15jq6x3dk9HFYHyuiYjY0xuDjWXx78qVK067qWHOHCA4GNi3zzHtz5jR1YcHZl8ZD3D7NuDnB3zwAfDA8u+I5dQpIDoauHmTbWoZSgbjc42Vn2A8Mp2djjlUtTvsgNX+4Uzlyy2wIo3OAzMkxiPzt791fdA5YkODBVaCon84syGxjQ0jH2ZIjEfG8gwIu0Ma/lg2njJDYgxHmCExHplr14CxY4Fuh7sPOcyQ+oflDsmZHptzdwdcXZkhOQPMkBiPTHl513SdI0tiM0PqH844ZScSsWeRnIWHPjqIYT8nTwLffefoXgw8ly4B//qvju2DSgWYTEBz89Af7jqScEZDArqm7UpLgWPHHN0T5+Txx4dmByMzpCGkW0V2p2PePMe23/20BmZIPdPYCLi4dE1xORMhIV1m9D//4+ieOCe7dgG/+tXgt8MMaQg5eRKYPt3RvRh4xoxx/Cnb3Q1p/HjH9mU442ylJyz86U/AIBw+zfgHQ/VLHjOkIcTL6587ghgDS/cSFIyecbZz7CyMGcP+bzkDbFMDwynoXoKC0TPOVguJ4VwwQ2I4BR4egFjMDKkvnPUOieEcMENiOAWWrb/MkHqHGRJjOMMMieE0KJVsDakvmCExhjMPZUg6nQ7x8fFQKpWQyWQICwvDO++8w7/+/PPPg+M4q6/Q0FCb+fLz8xEaGgqpVIqQkBBBru7cv38fa9euxbhx4yCXyxEdHY2ysjKb2nPnzmH+/PmQyWRQq9XYuHGjoGCfBSLCG2+8gaCgIEilUkyfPh2FhYU2c9bW1kKj0cDb2xteXl5YunQpvvnmm77eLsYQoVKxO6S+cNZddgznwO5ddn/5y18QHx+PmTNn4ne/+x3kcjmqqqpQXV0t0EkkEuTn56N7dQsvG3uD9+zZg9TUVCQlJWHz5s34/PPPkZaWBpPJhC3dHtwhIixZsgTl5eVIT0+HUqmEVqtFVFQUdDodJnZ7akuv12Px4sUIDQ1FTk4OqqurkZ2djZs3b+LEiROC9rdu3YqsrCysW7cOkZGRKC4uxooVK8BxnKASbFNTE6KiomA0GrFt2zaIxWLs3LkTUVFR0Ov18Pb2tvetZAwwbMqubxobgccec3QvGIwesKd40g8//EB+fn6UmJjYq+65554jDw+PPvOZTCZSqVQUHx8viK9atYo8PDyooaGBjx06dIhEIhEVFRXxsbt375K3tzetXLlScH1sbCwFBAQICvLl5eVZVbmtqakhV1dXSktLE1y/cOFCCgwMFBQgzMrKIo7jBMWoKioqSCwWU0ZGRq/jHA0F+oYD//ZvRLNmOboXw5sf/5ho40ZH94LhDAzG55pdU3YHDhzAnTt3sGPHDgBAc3Oz4A7oQTo7O2E0Gnt8/dSpU6ivr8f69esF8ZdeegmNjY2Cu5mjR4/Cz88Py5Yt42MqlQoajQbFxcUwm80AAKPRiJKSEqxevRqybvtbU1JSIJPJcPjwYT52/PhxtLe3IzU1VdB+amoqqqurcf78eUH7s2bNEhSimjx5MhYtWiTIyXAcrARF37A1JMZwxi5D+vTTT+Hp6Ylbt25hypQpkMvl8PT0xPr169Ha2irQNjc3w9PTE15eXlAqldiwYYPVGo5l/SciIkIQj4iIAMdxgvWhsrIym1UJZ8+ejebmZlRWVgIAysvL0d7ebpXTxcUF4eHhgpx6vR4ymQxTpkyxyklEvJaIcPXqVURGRtpsv6qqyub6FGNoYVN2fcMMiTGcscuQvv76a5jNZiQkJCA2NhZFRUV48cUXkZubixdeeIHX+fv7Iz09He+99x4KCwuRkJAArVaL2NhYdHZ28rq6ujqMGTMGKstTjf/AxcUFSqUStbW1Aq1arbbqkyVm0dbV1UEkEvWofTCnr69vnznr6+vR2trar/YZjkOpBH74AfjHzTLDBmxTA2M4Y9emhsbGRphMJqSmpiInJwcAsHTpUrS2tuLdd9/F9u3bMXHiRH5Kz4JGo0FwcDC2bduGI0eO8JsFTCYTXHs45VEikcBkMvE/m0wmuLm52dQREa+1fO9J29+c3XP1lbO7huE4LMcH1dcDNn7PGPW0twMtLeykBsbwxS5DkkqlAIBf/OIXgviKFSuwZ88enD9/XrDbrTubNm3Cb3/7W5SUlPCGJJVK0dbWZlPf0tLCt2fRPjgtaNGJRCJea/nek7a/Obvn6itnd01vbNq0yWqnYXJyMpKTk/u8ltE3lhttg4EZki2csVosY2goKChAQUGBIHZ/EE6ztcuQ/P39cf36datprnHjxgEAvv/++x6vlUgkUCqVqO9WRUutVqOjowMGg0EwbWc2m3Hv3j34+/sLtHV1dVZ5LTGLVq1Wg4h61D6Y8/Tp033mVCgUcHNz61f7vZGTk2NzHYwxMHQ/8ZthjbPWQmIMPrZ+cdbpdFZr9Y+KXWtIlsZramoEccv6iY+PT4/XNjY2wmAwCDTh4eEgIpSWlgq0ly9fRmdnJ8LDwwVanU5nlffChQtwd3dHSEgIAGDatGkQi8VWOc1mM/R6vVXO5uZmVFRUWOUUiUS8ViQSISwszConAFy8eBFBQUGCHX0Mx8AMqXeYITGGO3YZkkajAREhPz9fEN+7dy9cXFwQFRWF1tZWNFr+5Xdj+/btAIDY2Fg+Fh0dDYVCgd27dwu0u3fvhkwmQ1xcHB9LTEzE7du3UVRUxMcMBgOOHDmC+Ph4uLi4AAA8PT2xePFi7N+/X7Dzbd++fWhqahI87JqQkACxWAytVitoPzc3FwEBAZg7d66g/cuXLwtM8caNGzh58qQgJ8NxeHt3nWnHtn7bhk3ZMYY99j649OKLLxLHcbR8+XLSarWUlJREHMfRtm3biIjo22+/JW9vb1q/fj3t2rWLdu3aRUuWLCGRSERxcXFW+bRaLXEcR0lJSZSXl0cpKSnEcRxlZmYKdB0dHTRnzhzy9PSk7du3k1arpWnTppGXlxdVVlYKtDqdjqRSKc2cOZNyc3MpIyODpFIpxcbGWrWfnp5OHMfRunXrKC8vj+Li4ojjOCosLBTojEYjTZo0iXx9fSk7O5tycnIoMDCQxo8fTwaDodf3jD0YO3QoFES//72jezE8+ewzIoDoxg1H94ThDAzG55rdhtTe3k7bt2+nCRMmkJubG4WEhNCuXbv41xsaGiglJYVCQkJILpeTVCqlsLAwysrKovb2dps58/LyaOrUqSSRSCg4OFiQrzsNDQ20Zs0a8vHxIblcTtHR0aTT6Wxqz549S/Pnzyd3d3fy9fWltLQ0wckN3cnMzKQJEyaQRCKhsLAwKigosKmrqakhjUZDY8eOJU9PT0pISKCqqqre3i4iYoY0lAQHE/3mN47uxfDkxIkuQ6qpcXRPGM7AYHyuiYh6OWqBMSBYFv+uXLnCNjUMMnPmAFOnAv/v/zm6J8OPw4eB5cu7Sn17ejq6N4yRzmB8rrHyEwyngpWg6BnL0i7bf8MYrjBDYjgVrARFzzQ1AVIpMGaMo3vCYNiGGRLDqWDn2fVMYyO7O2IMb5ghMZwKZkg9ww5WZQx3mCExnAqVqussu25n+DL+ATMkxnCHGRLDqVAqu8yoocHRPRl+MENiDHeYITGcCnZ8UM+w0hOM4Q4zJIZTwQypZ9imBsZwhxkSw6noXoKCIYRN2TGGO8yQGE4Fu0PqGWZIjOEOMySGU+Hq2vWhywzJGmZIjOEOMySG08GeRbIN29TAGO48lCHpdDrEx8dDqVRCJpMhLCwM77zzjkBTUVGBmJgYeHh4QKlUIiUlBYYeJvbz8/MRGhoKqVSKkJAQq1wW7t+/j7Vr12LcuHGQy+WIjo5GWVmZTe25c+cwf/58yGQyqNVqbNy4UVAfyQIR4Y033kBQUBCkUimmT5+OwsJCmzlra2uh0Wjg7e0NLy8vLF26FN98801vbxXDAahUbA3JFuwOiTHcsauEOQD85S9/QXx8PGbOnInf/e53kMvlqKqqQnV1Na+pqanBggUL4O3tjczMTBiNRmRnZ+PatWu4dOkSxOJ/Nrtnzx6kpqYiKSkJmzdvxueff460tDSYTCZs2bKF1xERlixZgvLycqSnp0OpVEKr1SIqKgo6nQ4TJ07ktXq9HosXL0ZoaChycnJQXV2N7Oxs3Lx5EydOnBCMZ+vWrcjKysK6desQGRmJ4uJirFixAhzHCQrvNTU1ISoqCkajEdu2bYNYLMbOnTsRFRUFvV4Pb29ve99KxiDB7pCsIWK77BgjAHtqVfzwww/k5+dHiYmJvepSU1NJJpNRdXU1HyspKSGRSER79+7lYyaTiVQqFcXHxwuuX7VqFXl4eFBDQwMfO3ToEIlEIioqKuJjd+/eJW9vb1q5cqXg+tjYWAoICBDUP8rLyyOO4+iTTz7hYzU1NeTq6kppaWmC6xcuXEiBgYHU2dnJx7KysojjOEHtj4qKChKLxZSRkdHr+8HqIQ0tyclEUVGO7sXwoqWlqxbSvn2O7gnDWRiMzzW7puwOHDiAO3fuYMeOHQCA5uZmkI1ySkVFRXjyyScREBDAxxYtWoSQkBAcPnyYj506dQr19fVYv3694PqXXnoJjY2NgruZo0ePws/PD8uWLeNjKpUKGo0GxcXFMJvNAACj0YiSkhKsXr0asm6/DqakpEAmkwnaP378ONrb25GamipoPzU1FdXV1Th//ryg/VmzZgnqfkyePBmLFi0S5GQ4HlaCwhpL6Qk2ZccYzthlSJ9++ik8PT1x69YtTJkyBXK5HJ6enli/fj1aW1sBdK2z3LlzB5GRkVbXz549W7DmY/lzRESEQBcREQGO46y0topAzZ49G83NzaisrAQAlJeXo7293Sqni4sLwsPDBTn1ej1kMhmmTJlilZOIeC0R4erVqz2Oqaqqyub6FMMxsBIU1jBDYowE7DKkr7/+GmazGQkJCYiNjUVRURFefPFF5Obm4oUXXgAA1NXVAQDUarXV9Wq1GvX19fzdTF1dHcaMGQOV5WnGf+Di4gKlUona2lo+VldX12NOALy2rq4OIpGoR+2DOX19ffvMWV9fj9bW1n61z3A8ljUkVgv5n1h+X2KGxBjO2LWpobGxESaTCampqcjJyQEALF26FK2trXj33Xexfft2mEwmAICbm5vV9RKJBABgMpng4uICk8kEV1dXm21JJBI+l+WannISEa/tq/3+5uyeq79jYgwPlEqgrY1tc+4OqxbLGAnYdYcklUoBAL/4xS8E8RUrVoCIcP78eV5jmcLrTktLiyCPVCpFW1ubzbZaWlp4nUXbU06RSCTI2Vv7/c35YD/7OyaG47Gc1sDWkf4Jm7JjjATsukPy9/fH9evXraa5xo0bBwD4/vvv+Sksy9Rdd+rq6qBQKODi4gKga7qro6MDBoNBMG1nNptx7949+Pv78zG1Wt1jTkvfLDoi6lH7YM7Tp0/3mVOhUMDNza1f7ffGpk2b4OXlJYglJycjOTm5z2sZ/cfyT+nePeCxxxzalWEDMyTGo1BQUICCggJB7P79+wPejl2GFBERgZKSEtTU1CA4OJiPW9ZPxo0bB39/f/j4+KC0tNTq+kuXLiE8PJz/OTw8HESE0tJSxMTE8PHLly+js7PTSnvmzBmrnBcuXIC7uztCQkIAANOmTYNYLEZpaSkSExN5ndlshl6vx/LlywU58/PzUVFRIdjYcOHCBYhEIr59kUiEsLAwm2O6ePEigoKCBDv6eiInJ8fmxgzGwMLOs7OGGRLjUbD1i7NOp7PaPPao2DVlp9FoQETIz88XxPfu3QsXFxf89Kc/BQA888wz+PDDD1FTU8NrPv30U1RWVgoeNo2OjoZCocDu3bsF+Xbv3g2ZTIa4uDg+lpiYiNu3b6OoqIiPGQwGHDlyBPHx8fxdl6enJxYvXoz9+/cLdr7t27cPTU1NgvYTEhIgFouh1WoF7efm5iIgIABz584VtH/58mXodDo+duPGDZw8eVKQk+F4mCFZ09QEiEQAm1lmDGvsfXDpxRdfJI7jaPny5aTVaikpKYk4jqNt27bxmlu3bpGPjw9NmjSJ3n77bXr99ddJoVBQeHg4tbW1CfJptVriOI6SkpIoLy+PUlJSiOM4yszMFOg6Ojpozpw55OnpSdu3byetVkvTpk0jLy8vqqysFGh1Oh1JpVKaOXMm5ebmUkZGBkmlUoqNjbUaT3p6OnEcR+vWraO8vDyKi4sjjuOosLBQoDMajTRp0iTy9fWl7OxsysnJocDAQBo/fjwZDIZe3zP2YOzQ0tlJ5OZGtGuXo3syfNi5k0gud3QvGM7EYHyu2W1I7e3ttH37dpowYQK5ublRSEgI7bLxP//69esUExNDcrmcFAoFpaSk0J07d2zmzMvLo6lTp5JEIqHg4GCb+YiIGhoaaM2aNeTj40NyuZyio6NJp9PZ1J49e5bmz59P7u7u5OvrS2lpaYKTG7qTmZlJEyZMIIlEQmFhYVRQUGBTV1NTQxqNhsaOHUuenp6UkJBAVVVVNrXdYYY09Pj7E736qqN7MXzYvp3Iz8/RvWA4E4PxuSYiYk9rDDaWudYrV66wNaQh4vHHu6anfv5zR/dkeHDqFHDnDvD1147uCcNZGIzPNbsPV2UwRgKxscDhw8CBA47uyfBhyRJH94DB6B1mSAynJCur64vBYIwcWIE+BoPBYAwLmCExGAwGY1jADInBYDAYwwJmSAwGg8EYFjBDYjAYDMawgBkSg8FgMIYFzJAYDAaDMSxghsRgMBiMYQEzJAaDwWAMC5ghMRgMBmNYwAyJwWAwGMMCuwzps88+A8dxVl9jxozBpUuXeN3zzz9vUxcaGmozb35+PkJDQyGVShESEoJ33nnHpu7+/ftYu3Ytxo0bB7lcjujoaJSVldnUnjt3DvPnz4dMJoNarcbGjRsFBfssEBHeeOMNBAUFQSqVYvr06SgsLLSZs7a2FhqNBt7e3vDy8sLSpUvxzTff9PW2MRgMBqMfPNThqi+//DIiIyMFsUmTJgl+lkgkyM/PR/fqFl5eXla59uzZg9TUVCQlJWHz5s34/PPPkZaWBpPJhC1btvA6IsKSJUtQXl6O9PR0KJVKaLVaREVFQafTYeLEibxWr9dj8eLFCA0NRU5ODqqrq5GdnY2bN2/ixIkTgva3bt2KrKwsrFu3DpGRkSguLsaKFSvAcZygEmxTUxOioqJgNBqxbds2iMVi7Ny5E1FRUdDr9fD29n6Yt9LpKSgosCp9PBpg4x5djNZxDzj2FE86ffo0iUQiOnr0aK+65557jjw8PPrMZzKZSKVSUXx8vCC+atUq8vDwoIaGBj526NAhEolEVFRUxMfu3r1L3t7etHLlSsH1sbGxFBAQICjIl5eXRxzH0SeffMLHampqyNXVldLS0gTXL1y4kAIDA6mzs5OPZWVlEcdxgmJUFRUVJBaLKSMjo9dxjuYCfU899ZSju+AQ2LhHF6Nx3IPxufbQa0iNjY3o6OjoVdPZ2Qmj0djj66dOnUJ9fT3Wr18viL/00ktobGwU3M0cPXoUfn5+WLZsGR9TqVTQaDQoLi6G2WwGABiNRpSUlGD16tWQyWS8NiUlBTKZDIcPH+Zjx48fR3t7O1JTUwXtp6amorq6GufPnxe0P2vWLEEhqsmTJ2PRokWCnAwGg8F4OB7KkJ5//nl4enpCIpEgOjoaV65csdI0NzfD09MTXl5eUCqV2LBhg9UajmX9JyIiQhCPiIgAx3GC9aGysjKbVQlnz56N5uZmVFZWAgDKy8vR3t5uldPFxQXh4eGCnHq9HjKZDFOmTLHKSUS8lohw9epVq2lKi7aqqsrm+hSDwWAw+o9dhuTq6orExES89dZb+OCDD7Bjxw5cu3YNCxcuxBdffMHr/P39kZ6ejvfeew+FhYVISEiAVqtFbGwsOjs7eV1dXR3GjBkDlUolaMfFxQVKpRK1tbUCrVqttuqTJWbR1tXVQSQS9ah9MKevr2+fOevr69Ha2tqv9hkMBoPxcNi1qWHOnDmYM2cO//OTTz6JZ555Bo8//jj+/d//Hf/7v/8LANixY4fgOo1Gg+DgYGzbtg1HjhzhNwuYTCa4urrabEsikcBkMvE/m0wmuLm52dQREa+1fO9J29+c3XP1lbO7xhaW17766qseNc7K/fv3odPpHN2NIYeNe3QxGsdt+Tzr7bPPXh65hPnEiRORkJCAY8eOgYggEols6jZt2oTf/va3KCkp4Q1JKpWira3Npr6lpQVSqZT/WSqVorW11aZOJBLxWsv3nrT9zdk9V185u2ts8e233wIAVq1a1aPGmXlw+nS0wMY9uhit4/72228xb968Acn1yIYEAOPHj0dbWxuampogl8ttaiQSCZRKJerr6/mYWq1GR0cHDAaDYNrObDbj3r178Pf3F2jr6uqs8lpiFq1arQYR9ah9MOfp06f7zKlQKODm5tav9m3xxBNPYP/+/Xjsscd6NS4Gg8EYKZhMJnz77bd44oknBizngBhSVVUVJBJJj2YEdO3KMxgM8PHx4WPh4eEgIpSWliImJoaPX758GZ2dnQgPDxdoz5w5Y5X3woULcHd3R0hICABg2rRpEIvFKC0tRWJiIq8zm83Q6/VYvny5IGd+fj4qKioEGxsuXLgAkUjEty8SiRAWFobS0lKr9i9evIigoCDBjr4HUalUWLlyZY+vMxgMxkhkoO6MeOzZI3737l2rmF6vJ1dXV1q2bBkREbW0tJDRaLTSbdmyhTiOo+LiYj5mMplIqVTafA5JLpfT999/z8cOHTpEHMcJnoGyPIe0YsUKwfW9PYf0l7/8hY9VV1eTq6sr/epXvxJcv2DBAho/fny/n0PaunWr1XgZDAaDYR8iom5HKfTBokWLIJVKMXfuXIwbNw5ffvkl9u7dCzc3N5w7dw6TJ0/Gd999hxkzZiA5OZm/6/j444/x0UcfYcmSJfjwww8FOXfv3o0NGzbgmWeewRNPPIG//vWv2L9/P15//XW88sorvK6zsxPz58/Hl19+id/85jdQqVTQarW4desWLl++jODgYF5bVlaGefPmYerUqVi7di1u3brFn6pg2Xhh4ZVXXsGbb76JNWvWYNasWTh27Bg++ugjHDx4UHA31djYiBkzZsBoNOI3v/kNxGIxcnJy+O3hSqXSvt8EGAwGgyHEHvd6++236XwEm+MAAAdnSURBVCc/+QmpVCpydXWlgIAAevbZZ6mqqorXNDQ0UEpKCoWEhJBcLiepVEphYWGUlZVF7e3tNvPm5eXR1KlTSSKRUHBwMO3atcumrqGhgdasWUM+Pj4kl8spOjqadDqdTe3Zs2dp/vz55O7uTr6+vpSWlia4Y+pOZmYmTZgwgSQSCYWFhVFBQYFNXU1NDWk0Gho7dix5enpSQkKCYOwMBoPBeHjsukNiMBgMBmOwYOUnGAwGgzEsYIY0iLS1teGVV15BQEAA3N3d8ZOf/AQlJSWO7taA0dTUhFdffRWxsbFQKpXgOA779u2zqa2oqEBMTAw8PDygVCqRkpICg8EwxD0eGEpLS7FhwwZMmzYNcrkcP/rRj7B8+XJ8/fXXVlpnGvf169eh0WgwceJEyGQyKJVKzJ07FwcOHLDSOtO4H2THjh3gOA6PP/641WvONO7+lhsCBm7cA7Ltm2GbZ599FkVFRdi0aRMmTZqE9957D0uWLMHp06cxd+5cR3fvkTEYDHjttdfwox/9COHh4Taf6QKAmpoaLFiwAN7e3sjMzITRaER2djauXbuGS5cuQSweWf8Ms7KycO7cOSQlJeHxxx/H3//+d7z99tuYOXMmLl68yNf9crZxf/fdd2hsbMRzzz0Hf39/NDc34+jRo1i9ejW+++47bN26FYDzjbs7NTU1+P3vf2/zERdnHXdf5YYGdNyOXsRyVi5evEgikYh27tzJx1paWmjSpEk0b948B/Zs4Ghra6Pbt28TEVFpaSmJRCJ6//33rXSpqakkk8mourqaj5WUlJBIJKK9e/cOWX8HivPnz5PZbBbEvv76a5JIJLR69Wo+5mzjtkVnZyeFh4fTj370Iz7mzONevnw5LV68mKKioigsLEzwmrONu7/lhgZy3MyQBoktW7aQi4uL1TNZv//974njOMFfnjPQmyH5+vrS8uXLreKTJ0+mn//850PRvSEhIiKCIiMj+Z9Hy7ifeuopmjhxIv+zs477s88+IxcXF7p27ZpNQ3K2cXc3JKPR2OMu6YEcN1tDGiT0ej1CQkKsbu1nz57Nvz4aqK2txZ07d3os3dFTCfqRyO3bt/kjsJx53M3Nzbh37x7+7//+Dzk5Ofjzn//MPzPorOPu7OxEWloa1qxZgx//+MdWrzvruIHeyw0N9LhH5qTmCKC3chlENGrKVVjO+uvpvaivr4fZbIaLi8tQd21A2b9/P2pqavCf//mfAJx73Js3b8aePXsAdJWKeeutt7BmzRoAzjvu3bt3429/+xtOnjxp83VnHLel3NCSJUugUqlw/fp1vPnmm1i4cCHOnTuH6dOnD/i4mSENEv0tbeHs9Ld0x0j6j/ogFRUV2LBhA+bNm4eUlBQAzj3uTZs2ISkpCbW1tTh48CA2bNgAd3d3pKSkOOW46+vr8eqrr+J3v/sdFAqFTY0zjrs/5YYGetzMkAaJ/pa2cHYetXTHcOf27duIi4uDt7c3/vSnP/HlV5x53CEhIfxhxqtWrcITTzyBl19+GRqNxinHnZGRwVe97glnHLctHiw3NNDjZoY0SDxYndZCf8pVOBOWW/meSncoFIoR9Vtjd3744QfExMTghx9+wJkzZ+Dn58e/5szjfpDExESUlJSgoqLC6cZ98+ZN7N27F2+99RZqamoAAESElpYWmM1mfPfdd/D09HS6cfdG93JDAz1utqlhkAgPD0dlZSUaGxsF8QdLWzg7/v7+8PHxsVm649KlSyP2fWhtbcWTTz6Jmzdv4sSJE5g8ebLgdWcdty0s0zYcxznduGtqakBESEtLw4QJEzBhwgQEBQXh4sWLuHHjBoKCgvDaa6853bh7o3u5oQEft917ARn9wvIc0h/+8Ac+1traSsHBwTR37lwH9mxweNjnkN59992h7OaA0NHRQfHx8eTq6koff/xxjzpnG/edO3esYmazmWbOnEkqlYrfFuxM4zYYDFRcXGz1NW3aNHrsscfogw8+oGvXrhGRc42bqH/lhogGdtzscNVBZPny5Th+/Dhefvll/qSG0tJSnDx5cuALWzmI//qv/0JDQwNqamqQm5uLp59+GjNmzAAApKWlwcPDA9XV1Zg5cya8vLywceNGGI1GvPnmmwgMDMSlS5dG3FTGyy+/jF27diE+Ph5JSUlWr1uKMTrbuJ9++mn88MMPWLhwIQICAvD3v/8dBw4cwI0bN/Dee+9h9erVAJxv3Lb42c9+hnv37uHq1at8zNnG3Z9yQ8AAj/th3ZPRN62trZSenk7+/v4klUrpX/7lX+iTTz5xdLcGlMcee4w4jrP59d133/G669evU0xMDMnlclIoFJSSkmLzN+6RQFRUVI9j5jhOoHWmcR/6/+3doQ3EMBBFQeYKQtyEawgycKcpwrXtoUM5cCDgK5qBlsmiJ0uW9rpqzlm992qt1XEctdaqvfft7pvm/uU8zxpj3M7fNPc/64a+nprbCwmACD41ABBBkACIIEgARBAkACIIEgARBAmACIIEQARBAiCCIAEQQZAAiCBIAEQQJAAifABlSxtczGI/CAAAAABJRU5ErkJggg==",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x323488940>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(4,2))\n",
    "plot(m_)\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "ε = 1e-9; # Small float to avoid division by zero.\n",
    "m = (m_[2:end] .- m_[1:end-1]) ./ (m_[2:end] .+ m_[1:end-1] .+ ε);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326583438>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m = append!(m, 0)\n",
    "figure(figsize=(4,2))\n",
    "plot(m)\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward operator: convolution with wavelet\n",
    "\n",
    "Now we make the kernel matrix **G**, which represents convolution with a Ricker wavelet, plus a downsampling to ensure we are trying to solve an underdetermined problem, which is representative of many (most) inverse problems in geophysics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3268eaf60>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_, wavelet = ricker(100, 0.05, 0.001)\n",
    "figure(figsize=(4,2))\n",
    "plot(wavelet)\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use the `convmtx` function we defined earlier, selecting only the data we want — every other row, and only columns 26 to 75."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326d040b8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = convmtx(wavelet, size(m)[1])[1:2:end, 26:75]\n",
    "figure(figsize=(4,4))\n",
    "imshow(G,cmap=\"viridis\", interpolation=\"none\")\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "d = G * m;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x32691bfd0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure(figsize=(4,2))\n",
    "plot(d)\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Aside: an illustration of Gm = d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2awKpYX1Rahnc23ZNr4wc2zXJewfarpEka8se2zWZi722a7zPDLNdI0mjZky0XTP99gbbNZvKHrNdI0mVM0fYrnm25rqwnmtQzTbbNQlrNtquScvOsl0jSc1D7L8GmzISbde0JIf3vWi5wqgL76kAAACAc2JZlgKBVHX8htRQIJAiy7JkGLxpjSRmQAEAAAAAgJhkGIbc7kZ1PO3CktvdSPgUBQRQAAAAAAAgZhUVjZfLtbrdcy7XKhUXT4hyR/GJAAoAAAAAAMSsysr5ys9fKpdrpU7NhLLkcq1Ufv4yVVTc52R7cYMACgAAAAAAxCzTNOX11qq0dJ1yc29UdvbNys29UaWl6+T11so0TadbjAssQg4AAAAAAGKaaZryeBbJ4xELjjuEGVAAAADAOXrnnXdUWlqqSy+9VH369NHgwYM1ffp0ffLJJ23GfvTRRyosLJRpmkpPT9fs2bO1b98+B7oGEEsaGxu1cOFCTZkyRenp6XK5XHryySfbHRvv1yHCJ2cwAwoAAAA4R48++qjeeust3XbbbRo5cqR2796tX/ziFxozZozWrVunSy65RJK0Y8cOXX311erbt68WL14sv9+vn/3sZ/rggw+0fv169erF23MA4dm3b58efvhhDR48WKNHj9brr7/e7jiuQ3AKrywAAADgHN13332qqalp9YvbtGnT9N3vfleLFy8+OQuhsrJSTU1Neu+995SdnS1JGjt2rG644QYtX75c99xzjyP9A+j5srKytHv3bmVkZGjDhg0aO3Zsu+O4DkUPt/q1xi14AAAAwDm68sor28waGDp0qL7zne/I5/OdPPbiiy9q6tSpJ3/pk6Trr79ew4cP13PPPRe1fgHEHrfbrYyMjE7HcR2KLL/fr7KyhcrLm6ScnFuUlzdJZWUL5ff7nW7NcQRQAAAAQITs2bNH/fv3lyTt3LlTe/fu1RVXXNFm3Lhx47Rx48ZotwcgznAdiiy/36+CghJVVxfo88//oB07fqfPP/+DqqsLVFBQEvchFAEUAACS4aVsAAAgAElEQVQAEAFPPfWUduzYoRkzZkiSdu3aJUnKzMxsMzYzM1MHDhxQIBCIao8A4gvXochasKBKPt88BYOFkk7cemcoGCyUzzdX5eVLnGzPcbYDKFbWBwAAAM7so48+UmlpqcaPH6/Zs2dLkpqamiRJvXv3bjM+KSmp1RgAiASuQ5FVX79WweDkds8Fg4Wqq1sb5Y66F9uLkLOyfowKe100+4VWmM9kJdivCaTa769lcNuL8dnolZFjuyZ570DbNdaWPbZrJClzsdd2jfeZYbZrRs2YaLtGkqbf3mC7ZlPZY2E9V+XMEbZrnq25znbNoJpttmskKWGN/anPadlZtmuah9h//UlSU0ai7ZqW5PAuMpYrjDrWeQTgsD179ugf/uEf1LdvXz3//PMnF6BNTk6WJB09erRNzZEjR1qN6cjcuXOVlpbW6tjMmTM1c+bMrmgd3VhNTY1qampaHTt48KBD3aCn4joUOZZlKRBIVcdvRg0FAik9emHyc70O2U6BWFkfAAAAaN8333yjwsJCffPNN3rzzTd1wQUXnDx34paXE7fAnG7Xrl3q16+f3G73GT//smXLNGbMmK5tGj1Ce7/gv/vuu7r88ssd6gg9EdehyDEMQ253o0JTLtoLmCy53Y09NnySzv06ZPsWPFbWBwAAANo6evSopk6dqk8//VQvv/yyLr744lbns7KyNGDAAL3zzjttatevX6/Ro0dHq1UAcYrrUGQVFY2Xy7W63XMu1yoVF0+IckfdS0QWIWdlfQAAAMSTYDCoadOmad26dXrhhRc0bty4dseVlJTopZde0o4dO04ee+2117R582ZNmzYtWu0CiGNchyKnsnK+8vOXyuVaqVOLz1hyuVYqP3+ZKiruc7I9x0VkIaazXVm/s6l9AAAAQE8wb9481dfXq7i4WPv27dPTTz/d6vwdd9whSXrwwQf1wgsv6Nprr9W9994rv9+vqqoqjRo1SnfffbcDnQOIJdXV1fr6669Phkt1dXXati20LmlZWZlM0+Q6FEGmacrrrVV5+RLV1S1VIJAit/uwiovHq6KiVqZpOt2ioyISQJ3tyvoEUAAAAIgF77//vgzDUH19verr69ucPxFAXXjhhXrjjTc0b948PfDAA0pMTNTUqVNVVVXFe2MA56yqqkpffvmlpNCaRCtWrNCKFSskSbNmzZJpmlyHjnviiSc0Z84cGYahrVu3atCgQV3yeU3TlMezSB6PevSC45EQkQCqK1bWBwAAAHqKP/7xj2c9Nj8/XytXroxgNwDi1datW89qHNeh6CB8ai0iAVRXrKy/bf3vlJCY1OpYv7zL1G8Iq+0DAADg7BzY8q4ObG29/uix5iMOdQMAQPyKSADVFSvr54y7WSnpF0aiPQAAAMSJfkPGtPkD5uH92+WrX+ZQRwCA7sayrM4H4ZxFZBc8iZX1AQAAAABA99TU1CTLshQMBvV3f3eP8vImqaxsofx+v9OtxaywZkCxsj4AAAAAAOiJ/H6/Kir+Q5IhydCePb+WlKPq6tVqaCiR18uOdZEQVgDFyvoAAAAAAKC7+vrrr7V48WL97ne/0xdffCHTNDVy5Ej94Ac/0J/+9Bft3DlZ0oenVRgKBgvl81kqL18ij2eRQ53HrrACKFbWBwAAAAAA3ZHP59OkSZO0a9eukzvRHT16VA0NDXrttdeUmnqBLOun7dYGg4Wqq1sqjyeaHceHiCxCDpxR2DtR2i8MZyk5KyGMIkmBVPv9tQzubbumV0aO7RpJSt470HaNtWWP7ZrMxV7bNZLkfWaY7ZpRMyaG9VzTb2+wXbOp7DHbNZUzR9iukaRna66zXTOoZpvtmoQ1Gzsf1I607CzbNc1D7L/+JKkpI9F2TUtyGNcKV5gXJnbWRRdxGYb+fsxFKrg0V9+9KFP9zkvRealJOtIc0N/8Tfp0+z5t+nSnXnv7E+3a/43T7QIA0G35/X5NnjxZu3fvlmEYmjFjhmbPnq2MjAxt3rxZS5cu1fr16yV19P7eUCCQIsuyToZX6BoEUAAAAA66ZvQQ3Tv975WTcb4kyTrtzycpSYlKSUpU9oA0XXvZUJXddo3e3LRFv3h+jbbuPOBUywAAdFs/+clPtH37dhmGoUceeUT333//yXOXXXaZbr31VvXpk6EjR97u4DNYcrsbCZ8igAAKAADAId8r+jv98y0FMmTIkqUNH23Xm+9v0SfbvtLBQ0eU1LuX+qf10WUXZ+vqUUOU2f88jR+Zpz0H/Hr0N/ZncwIAEMsCgYD+93//V4ZhaOTIka3CpxMSEhI0c+ZsPf74f0g61ua8y7VKxcUTotBt/CGAAgAAcEDx1d/RD265SpYs7T/YqAcee1nvfbKj3bENGz7Rkt++rhvHXaz/WzI+uo0CANBDbNiwQX/7299kGIbuuuuuDsd5PD/R888/pUOH9p921JLLtUr5+ctUUVEb+WbjkMvpBgAAAOJNRt8+uv+OibJkqbGpWd/76TMdhk+ne2X9x7p94W/05vtntyEMAADx5C9/+cvJx2PHju1wnGmauvfeHyi0anBQAwd+T7m5N6q0dJ283lqZphn5ZuMQARQAAECU3Tn5ciW6QxPRq2vf1M59Z7+w+OEjAa3dRAAFZ/z4xz+Wy+VSQkJo15ZDhw7pJz/5iUaOHCnTNDVw4EBNmTJFf/rTn1rVffXVVyovL9ell16qPn36qH///rr55pu1cWN4G2IAQHsOHDi1PmJGRsYZxw4aNEiGYcjlcmndul9p69Y/yONZRPgUQdyCBwAAEGVTrsqXJB0+0qyX3vzQ4W6A8Gzfvl2TJk3S5s2bTy7We/jwYa1evVp/+MMf9MQTT+iOO+7Qxo0bVVRUpF27dp2sbWpqUn19vV555RWtXLlS1157rUNfBYBYZWcRcRYcjw5mQAEAAETRRdnpSktNliVLGzfv0NFAi9MtAWG57bbbtGPHDi1YsEBvvPGG3n77bS1btkxpaWkKBoP6l3/5F3388ceaOnWqjh49qp/+9Kd68803tW7dOv34xz9W79691dzcrDlz5qilhe8DAOeub9++Jx/v2bPnjGM7O4+uxwwoAACAKBqaM+Dk44++2OtgJ0D4LMvS+++/rz/96U+64oorTh4fM2aMhg4dqqlTp+rw4cMqKCiQ2+3W22+/rdzc3JPjrrjiCqWnp+tf//Vf9eWXX+rll19Wnz43O/CVAJLLde7zMpYvX67Zs2d3QTc4F9/97ndPPn777bc1fnzHG3e8/fbb0WgJp2EGFAAAQBSd3yf55OOv/U1nHDskK73DDxe3C8BBhmFo7ty5rcKnE2666SYNHjxYlmXp4MGDqqioaBU+nTBnzhwlJSVJktasWRPploEOGYZxzh+IHMuyznrs5ZdffnIW1G9+85sOx+3YsUOvvPLKOfcGe5gBBQAAEEWpSe6Tj5uOBjoel5yoZx5u/6/pliwV/3+/1p4D/i7vDzhb06dP7/DcyJEj9cUXX8gwDE2bNq3dMUlJSRo2bJg++OADbdmyJVJtAp06fee0cF144YVd0AlO8Pv9WrCgSvX1axUIpMrtblRR0XhVVs4/4yLhiYmJmjNnjpYuXar33ntPVVVVmj9/fqsxx44d0/e//30FAh3/DEZkEEABAABEUeORU294k3u7zzAyFDR9myH+0o7uYfjw4R2eO//88yVJ/fv3V1pa2hnHWZYlv58wFc655JJLnG4Bp/H7/SooKJHPN0/B4CJJhiRL1dWr1dBQIq+39owh1EMPPaTnnntO27dv1/3336+NGzdq9uzZysjI0ObNm7VkyRJt2LBBV1xxBbfhRRkBFAAAQBQdPHTqtrvzzeQOxzU2NevvvvfzVsce+j83aur470SsN8COE7fPtefEmjopKSln/Bwnxh07dqzrGgPQoy1YUHU8fCo87aihYLBQPp+l8vIl8ngWdVh/3nnnadWqVbrhhhu0e/du1dTUqKam5tRnMgzNmTNHV199tebMmRO5LwRtEEABAABE0Sfbvjr5eMSgDAc7AQBI0l//+tdz/hwXXnjhGWf74ezV1689PvOprWCwUHV1S+XxnPlzXHLJJfrrX/+qRx99VCtWrNCXX34p0zT13e9+V//8z/+sadOm6YknnmANrygjgEJsC+taEt4F6OyXxjutJsF+TSA1vP5aBve2XdMrI8d2TfLegbZrJMnaYn8b1MzF3rCey/vMMNs1o2ZMtF0z/fYG2zWStKnsMds1lTNH2K55tuY62zWSNKhmm+2ahDUbw3qutOws2zXNQ+y/BpsyEm3XSFJLsv3vR8sVxvcw74tiymc79utgY5PSUpM1eni2EnslqLmF2R8A4JTTd04LF7vgdQ3LshQIpKrjNz+GAoEUWZbVaXB0/vnn65FHHtEjjzzS7vm77rpLd91117k1DFvYBQ8AACDKVr7lkxRaaHzqBNYeAQAnnesOeCduJcW5MwxDbnejOv7zviW3u5FZSz0U3ykAAABR9vQrG9QcaJEhQ/9acrUuSO94MVUAQGQdO3bsnD5aWlqY/dSFiorGy+Va3e45l2uViosnRLkjdBUCKAAAgCjbc+CQfvbbP0qSzJTe+vWDMzRqaOe3nJopHS/6DABALKisnK/8/KVyuVbq1EwoSy7XSuXnL1NFxX1OtodzwBpQAAAADvjdnz7QgPP76Ps3X6n+56fqfx6Yrrd9X2rN+1v06fZ9+ubQEblchtLTUjVicIZuGHexhmSlS5KOHQuqhXWjECO4lQbA6UzTlNdbq/LyJaqrW6pAIEVu92EVF49XRUWtTJNZwz0VARQAAIBDflX3Z32y7SvdO/0aZQ9I0xX5ORqbP6jdsZYsBS1L3r98Ls9zf9L+bw5HuVsgMiwrnK1cAMQy0zTl8SySx6OzWnAcPQMBFAAAgIPe2PiZ/vTeZ7puzDBdeelgjRyapb5mssyU3jrS3KKDh47o0+379JfPduqV9R9r936/0y0jzp3ttuVdPQ5AfOL6EDsIoAAAABxmWVLDhk/UsOETp1sBzmjhwoVauHBhp+Mef/xxPf74452O++Mf/3jy8WuvnVNrAIBujkXIAQAAAAAAbOD2YfsIoAAAAAAAADrh9/tVVrZQeXmTlJNzi/LyJqmsbKH8fm6PPxvcggcAAAAAAHAGfr9fBQUl8vnmKRhcJMmQZKm6erUaGkrk9bJDX2eYAQUAAAAAAHAGCxZUHQ+fChUKnyTJUDBYKJ9vrsrLlzjZXo9AAAUAAACg2/j5z6X/+i/pd7+T3n5b2r5dCgSc7gpAvKuvX6tgcHK754LBQtXVrY1yRz0Pt+ABXSWs3UHtF4W71J2VYL8mkGq/v5bBve0/kaReGTm2a5L3Dgzruawte2zXZC722q7xPjPMdo0kjZox0XbN9NsbbNdsKnvMdo0kVc4cYbvm2ZrrwnquQTXbbNckrNlouyYtO8t2jSQ1D7H/GmzKSLRd05Ic3vbDliuMOnY6BuCQiy+WrrpKev55ac8e6dixU+cMQxowQMrMlLKyWv97+uMLLpAS7V9mAeCMLMtSIJCqjt8oGQoEUmRZlgyDN1MdIYACAAAA4LgLL5TWHp9AcOyY9NVX0q5doY+dO1s//uAD6Q9/CP13S0vrz9O/f8cB1emPe4f3NzMAccgwDLndjQpNB2gvYLLkdjcSPnWCAAoAAABAt5KQEJrNdMEF0mWXdTwuGJT2728bUJ3496OPpD/+MfTfzc2ta/v1O3NAdeLf5OTIfq0AeoaiovGqrl59fA2o1lyuVSounuBAVz0LARQAAACAHsnlCt2aN2CANGpUx+MsSzpwoG1AdSK0+vRTac2a0OMjR1rXpqWdOaA68Tg1NbJfKwBnVVbOV0NDiXw+67SFyC25XKuUn79MFRW1TrfY7RFAAQAAAIhphiGlp4c+Lr2043GWJX39dfu3/e3aJX3xhfTnP4f+u6mpda1pdn7bX1ZWaByAnsc0TXm9tSovX6K6uqUKBFLkdh9WcfF4VVTUyuSbu1MEUAAAAACgUFDVt2/o45JLOh5nWdI337R/29+Jf995J/T40KHWtampnd/2l5kZmnnFcjJA92KapjyeRfJ4xILjYSCAAgAAAAAbDCMUEKWlSSM62RzW728bVG3bJr3/vrRqlXTwYPt1KSnSk09KJSVd3z+Ac0f4ZB8BFAAAAAB0gUBA2rOn/dv3Tn+8d29oAfUTXC4pI6PtrKixY537WgCgqxFAAQAAAMAZHD0q7d595lBp1y7pq69Ct+edcGI3vxOh0rhx7d92N2CA1IvfzAB0U111uyGXOQAAAABx6ciRzkOlnTul/ftb17ndp4KlrCzpqqvaX8upf/9QCAUAPY3f79eCBVWqr1+rQCBVbnejiorGq7JyftgLrhNAAQAAAIgphw93Hirt2iX97W+t6xITWwdI11zT/gLh6emh2+YAIBb5/X4VFJTI55unYHCRJEOSperq1WpoKJHXG96ufwRQAAAAAHqEQ4c6D5V27Wq7sHdSUusA6ZJL2t+Jrm9fdp4DgAULqo6HT4WnHTUUDBbK57NUXr5EHs8i25+XAAoAAACA4yxL8nqlrVs7DpgOHWpdk5LSeobSqFFtQ6XMzNBudQRLAHB26uvXHp/51FYwWKi6uqXyeOx/XgIooKcJ+82T/UKr8yFta8Jc5yCQar+/lsG9w3quXhk5tmuS9w60XWNt2WO7RpIyF3tt13ifGWa7ZtSMibZrJGn67Q22azaVPRbWc1XO7GRv63Y8W3Od7ZpBNdts10hSwpqNtmvSsrNs1zQPsf/6k6SmjETbNS3J4V1kLFcYdfwyCOA0Xq80fnzosWm2DpauuKJtqJSZGRpHsAQAXceyLAUCqer4jZqhQCAlrIXJCaAAAAAAOK6pKfTvhx9K+fnO9gIA8cowDLndjQpNR2gvYLLkdjeGtSseS+cBAAAA6DaSk53uAADiW1HReLlcq9s953KtUnHxhLA+LwEUAAAAAAAAJEmVlfOVn79ULtdKnVqYxZLLtVL5+ctUUXFfWJ+XAAoAAAAAAACSJNM05fXWqrR0nXJzb1R29s3Kzb1RpaXr5PXWyjTNsD4va0ABAAAAAADgJNM05fEsksejsBYcbw8zoAAAAIBz9OGHH2ratGm66KKLlJqaqvT0dF111VV6+umn24z96KOPVFhYKNM0lZ6ertmzZ2vfvn0OdA0gljQ2NmrhwoWaMmWK0tPT5XK59OSTT7YZN2fOHLlcrjYfl1xyiQNdoyfoivBJYgYUAAAAcM6++OILHTp0SHfffbeysrJ0+PBh1dbWatasWfriiy/04IMPSpJ27Nihq6++Wn379tXixYvl9/v1s5/9TB988IHWr1+vXr14ew4gPPv27dPDDz+swYMHa/To0Xr99dc7HJuUlKRf//rXsizr5LG0tLQodIl4xk84AAAA4BxNmTJFU6ZMaXWstLRUY8aM0S9/+cuTAVRlZaWampr03nvvKTs7W5I0duxY3XDDDVq+fLnuueeeqPcOIDZkZWVp9+7dysjI0IYNGzR27NgOx/bq1UszZ86MYncAt+ABAAAAEWEYhnJyclrNanrxxRc1derUk+GTJF1//fUaPny4nnvuOSfaBBAj3G63MjIyznp8MBiU3++PYEfx6/SZZTiFAAoAAADoIocPH9b+/fu1ZcsWLVu2TKtXr9aPfvQjSdLOnTu1d+9eXXHFFW3qxo0bp40bN0a7XQBx6vDhwzrvvPOUlpam9PR0lZaWqrGx0em2ejS/36+ysoXKy5uknJxblJc3SWVlCwn5TsMteAAAAEAXue+++/Tf//3fkkKzETwej77//e9Lknbt2iVJyszMbFOXmZmpAwcOKBAIyO12R69hAHEnKytL999/v8aMGaNgMKhVq1bpP//zP7Vp0ya9/vrrcrmYp2KX3+9XQUGJfL55CgYXSTIkWaquXq2GhhJ5vbUyTdPhLp1HAAUAAAB0kblz5+q2227Tzp079dvf/lalpaVKSUnR7Nmz1dTUJEnq3bt3m7qkpCRJUlNTEwEUgIiqrKxs9d/Tpk3TsGHDVF5erhdeeEHTpk1zqLOea8GCquPhU+FpRw0Fg4Xy+SyVly+Rx7PIqfa6DdvRJls7AgAAAO0bPny4Jk6cqDvvvFO///3vdf311+uHP/yhjhw5ouTkZEnS0aNH29QdOXJEkk6OAYBomjt3rgzD0Kuvvup0Kz1Sff1aBYOT2z0XDBaqrm5tlDvqnmzPgGJrRyCOGFErUjjL9FkJYT2VAqn2e2wZ3Pav1Z3plZFju0aSkvcOtF1jbdljuyZzsdd2jSR5nxlmu2bUjIlhPdf02xts12wqe8x2TeXMEbZrJOnZmuts1wyq2Wa7JmFNeOvCpGVn2a5pHmL/9SdJTRmJtmtaku1/L1qu8K4xYV6agHN266236tVXX9VHH3108ta7E7finW7Xrl3q169fp7Of5s6d2+b99MyZM9nNKg7U1NSopqam1bGDBw861A1iTVJSktLT03XgwIFOx3Idas2yLAUCqer4zYahQCBFlmXJMHr2G5JzvQ7ZDqDY2hEAAAA4Oyduu3O5XMrKytKAAQP0zjvvtBm3fv16jR49utPPt2zZMo0ZM6bL+0T3194v+O+++64uv/xyhzpCLDl06JD27dunAQMGdDqW61BrhmHI7W5U6E/q7QVMltzuxh4fPknnfh2yfQseWzsCAAAArX311VdtjrW0tOiJJ55Qv3799J3vfEeSVFJSopdeekk7duw4Oe61117T5s2bWXcFQMQdPXpUhw4danP8Jz/5iSRpypQp0W4pJhQVjZfLtbrdcy7XKhUXT4hyR91TRBchP7G14+HDh9W3b1/NnDlTjz76qFJTUyP5tAAAAEBU/eAHP9A333yja665RtnZ2dq9e7eefvppffzxx1q+fLkSEkL3jT/44IN64YUXdO211+ree++V3+9XVVWVRo0apbvvvtvZLwJAj1ddXa2vv/76ZMhdV1enbdtCt/+XlZXpwIEDuuyyyzRz5kyNGBFagmDVqlVauXKlbrrpJhUXFzvWe09WWTlfDQ0l8vms4wuRh3bBc7lWKT9/mSoqap1usVuIWADF1o4AAACIFzNmzNCvf/1r/dd//Zf279+v8847T+PGjdN//Md/aOLEU+vgXXjhhXrjjTc0b948PfDAA0pMTNTUqVNVVVXF7ncAzllVVZW+/PJLSaFbw1asWKEVK1ZIkmbNmqXzzz9fRUVFevXVV/Xkk0/q2LFjGjp0qBYvXqz77rvPydZ7NNM05fXWqrx8ierqlioQSJHbfVjFxeNVUVEr0zSdbrFbiFgAxdaOAAAAiBfTpk076/e3+fn5WrlyZYQ7AhCPtm7d2umYJ554IgqdxB/TNOXxLJLHo5hYcDwSInoL3rfNnTtX//Zv/6ZXX3210x/Q29b/TgmJSa2O9cu7TP2GsNgZAAAAzs6BLe/qwNbWO0keaz7iUDcAgHhA+NS+qAZQdrZ2zBl3s1LSL4xCVwAAAIhV/YaMafMHzMP7t8tXv8yhjgAAiE9RXYjJztaOAAAAAAAA58qyLKdbgCIUQLG1IwAAAAAAcIrf71dZ2ULl5U1STs4tysubpLKyhfL7/U63FrfCugWPrR0BAAAAAEB35Pf7VVBQIp9vnoLBRZIMSZaqq1eroaFEXi870zkhrACKrR0BAAAAAEB3tGBB1fHwqfC0o4aCwUL5fJbKy5fI41nkVHtxK6wAiq0dAQAAAABAd1Rfv/b4zKe2gsFC1dUtlccT3Z4Q5V3wAKBDYe1UGt72puEsQWgl2K8JpIbXX8vg3rZremXk2K5J3jvQdo0kWVv22K7JXOwN67m8zwyzXTNqxkTbNdNvb7BdI0mbyh6zXVM5c4TtmmdrrrNdI0mDarbZrklYs7HzQe1Iy86yXdM8xP5rsCkj0XaNJLUk2/9+tFxhfA+z6zIAAI6yLEuBQKo6/qFsKBBIkWVZMgx+cEdTVHfBAwAAAAAAiBTDMOR2N6rjPztbcrsbCZ8cQAAFAAAAAABiRlHReLlcq9s953KtUnHxhCh3BIkACgAAAAAAxJDKyvnKz18ql2ulTs2EsuRyrVR+/jJVVLA5mhMIoAAAAAAAQMwwTVNeb61KS9cpN/dGZWffrNzcG1Vauk5eb61M03S6xbjEIuQAAAAAACCmmKYpj2eRPB6x4Hg3wQwoAAAAAAAQswifugcCKAAAAAAAAEQUARQAAAAAAAAiigAKAAAAAAD0eJZldT4IjiGAAgAAAAAAPZLf71dZ2ULl5U1STs4tysubpLKyhfL7/U63hm9hFzwAAAAAANDj+P1+FRSUyOebp2BwkSRDkqXq6tVqaCiR11sr0zQd7hInMAMKAAAAgOOOHXO6AwA9zYIFVcfDp0KFwidJMhQMFsrnm6vy8iVOtodvYQYUAAAAgKjx+6WPPpI+/FDy+UIfH34obdkSOp+c7Gx/AHqO+vq1x2c+tRUMFqqubqk8nuj2hI4RQAGIP0bnQ7qiKNwlEK0E+zWBVPv9tQzubf+JJPXKyLFdk7x3YFjPZW3ZY7smc7HXdo33mWG2ayRp1IyJtmum395gu2ZT2WO2aySpcuYI2zXP1lwX1nMNqtlmuyZhzUbbNWnZWbZrJKl5iP3XYFNGou2aluSwLjCyXGHUhfdUQNTs23cqXDo9aNq+/dSYQYOk/HypqCj07+WXSwPD+5EBIM5YlqVAIFUd/0A0FAikyLIsGQY/NLsDAigAAPD/t3f3wVHV9x7HP7thISEsDATQEEMejEgAAakyxKgjD0rUEB0DQXygOmpneme7AnF0FCrMNRlxjOBqU9o63kEGJoo8XUIFppAqBdZkqCi1LgpXRQ0hFNLKEgJZ2HP/CATS3RRPyO4mu+/XzJni+f2+ni+dnyeb7/4eAKBDDEOqrQ1eaDp2rKVPXJx07bXSiBHSo4+2FJpGjJCuv17q0yey+QPoviwWi2y2RrV87RuswGTIZmuk+C2piyIAACAASURBVNSFUIACAAAA8B+dOyd9801gocnjaVlSJ0m9erUUlUaMkCZPvlhoyspqaQOAzjZtWq7Ky7ee3wOqLat1iwoKbo1AVmgPBSgAAAAAkqQzZ6QDBwILTV9+2dImSXb7xeJSYeHFP6ent8x2AoBwKS19RlVVhfJ4jEs2IjdktW5RdvZSlZSsjXSKuAQFKAAAACDGnDzZshH4vxea/u//Lp5GN2hQS3HpllukJ564WGgaMkRiRQuArsBut8vtXqsFC17Txo1L5PP1ls12SgUFuSopWSu73R7pFHEJClAAAABAlPvb36T/+Z+LhabvvrvYlpraUli6556WItOFa+DAyOULAD+V3W6Xy7VILpfYcLyLowAFAAAARLnt26U337w4u0mS+vaV7r1XuvnmlgJUdnZLMYrf3QB0VxSfujYKUAAAAECUmzNH+q//kg4eDFx2t369dPp0S7/ExLazoC4UpjIzpR785gAAuAL8GAEAAABiQM+eLQWlC5uHX3DunHTo0MWC1IXi1MaN0o8/XowdNiywODVsmBQfH5m/D4DuheVxoAAFAAAAxLC4uJYZTpmZLUvyLjAMqa4usDC1Y4dUX9/Sx2qVMjIuzpS6UJgaPrxliR+A2Ob1ejV/fpkqK3fJ50uUzdaoadNyVVr6DBuExyAKUAAAAAACWCwtJ94NGSJNnty2raHhYmHqQnHqvfdaZlJdkJISWJjKzm45XQ9A9PN6vcrJKZTHM09+/yJJFkmGysu3qqqqUG43p9TFGgpQAAAAAEwZMEDKzW25LtXYKO3f37YwtXWrVF5+cQP0pKS2BakLf77mGjZAB6LJ/Pll54tPeZfctcjvz5PHY2jBgtfkci2KVHqIAApQAAAAADpFYqL0s5+1XJdqbpYOHGhbmKqullasuLgBep8+0k03SR98ICUkhD93AJ2rsnLX+ZlPgfz+PG3cuEQuV3hzQmRRgAKAUOnwt7jmA40OPMWI60CQJF+i+fzOpvXq0LN6DE41HZNw9CrTMcbX9aZjJCl5sdt0jPvd60zHjHlwkukYSZr5UJXpmH3OZR16Vums4aZj3quYaDpmaMX3pmMkKe4ve03H9EsZYjqmOdP8+JOkpsE9TcecTejAu8LawRcTs1JwhXr2lEaObLkude6c9O23LUWpDz6Qli1r2V8qPT0SWQLoLIZhyOdLVPs/QCzy+XqzMXmMoQAFAAAAICLi4qRrr225EhJaClAAuj+LxSKbrVEtX5MGKzAZstkaKT7FGGukEwAAAAAAANFl2rRcWa1bg7ZZrVtUUHBrmDNCpFGAAgAAAAAAnaq09BllZy+R1bpZFzeMMGS1blZ29lKVlBRHMj1EAAUoAAAAAADQqex2u9zutXI4qpWefpdSUu5Tevpdcjiq5Xavld1uj3SKCDP2gAIAAAAAAJ3ObrfL5Vokl0tsOA5mQAEAAAAAgNCi+AQKUAAAAAAAAAgpClAAAAAAACDmGIZx+U7oNBSgAAAAAABATPB6vXI6FyojY4pSU+9XRsYUOZ0L5fV6I51a1GMTcgAAAAAAEPW8Xq9ycgrl8cyT379IkkWSofLyraqqKuR0vhBjBhQAAAAAAIh68+eXnS8+5aml+CRJFvn9efJ45mrBgtcimV7UowAFAAAAAACiXmXlLvn9U4O2+f152rhxV5gzii0swQOAaNChU207dhRuR7ZqNOI69Cj5Es3neDatl+mYHoNTTcdIUsLRq0zHGF/Xm45JXuw2HSNJ7nevMx0z5sFJHXrWzIeqTMfscy4zHVM6a7jpGEl6r2Ki6ZihFd+bjon7y17TMZLUL2WI6ZjmTPPjr2lwT9MxknQ2wfx/i4a1g8dtc0o3ACAEDMOQz5eo9n/QWOTz9ZZhGLJY+GEUCsyAAgAAAAAAUc1ischma1T7X6castkaKT6FEAUoAAAAAAAQ9aZNy5XVujVom9W6RQUFt4Y5o9hCAQoAAAAAAES90tJnlJ29RFbrZl2cCWXIat2s7OylKikpjmR6UY8CFAAAAAAAiHp2u11u91o5HNVKT79LKSn3KT39Ljkc1XK718put0c6xajGJuQAAAAAACAm2O12uVyL5HKJDcfDjBlQAAAAQCcrLS2V1WrV6NGjA9r279+vvLw82e12JSUlafbs2Tp27FgEsgQQTfbs2SOHw6FRo0apT58+SktL08yZM3XgwIGAvryHWlB8Ci9mQAEAAACdqLa2Vi+//LL69OkTtO22225T//79tXjxYnm9Xr366qv6/PPPVVNTox49+HgOoGNeeeUV7d69WzNmzNDo0aN15MgRvfnmmxo3bpyqq6s1YsQISbyHEDmMLAAAAKATFRcXKycnR2fPntXx48fbtJWWlqqpqUmffvqpUlJSJEk333yz7rzzTi1fvlxPPvlkJFIGEAWKi4tVUVHRpoBUVFSkG264QYsXL9aKFSsk8R5C5LAEDwAAAOgkO3bs0Lp16/T6668HbV+3bp3y8/Nbf+mTpMmTJ2vYsGFavXp1uNIEEIUmTJgQMHspKytLI0eOlMfjab3Heyh8DMO4fKcYQgEKAAAA6AR+v19Op1NPPfWURo4cGdB++PBhHT16VDfddFNA2/jx47V3795wpAkgxtTX12vgwIGSeA+Fg9frldO5UBkZU5Saer8yMqbI6Vwor9cb6dQijiV4AAAAQCdYtmyZvvvuO1VVVQVtr6urkyQlJycHtCUnJ6uhoUE+n082my2keQKIHStXrlRtba1KSkok8R4KNa/Xq5ycQnk88+T3L5JkkWSovHyrqqoK5Xavld1uj3CWkcMMKAAAAOAKNTQ0aOHChXrxxRc1YMCAoH2ampokSb169Qpoi4+Pb9MHAK7U/v375XA4lJubq9mzZ0viPRRq8+eXnS8+5aml+CRJFvn9efJ45mrBgtcimV7EmSpAcawjAAAAEGj+/PlKSkqSw+Fot09CQoIk6cyZMwFtp0+fbtMHAK5EfX297r33XvXv31/vv/++LJaWYgjvodCqrNwlv39q0Da/P08bN+4Kc0Zdi6kleBzrCABo/TIn9EHqyLaNRpz5GF9ix/I7mxb47eHl9Bicajom4ehVpmMkyfi63nRM8mJ3h57lfvc60zFjHpxkOmbmQ8GXNl3OPucy0zGls4abjnmvYqLpGEkaWvG96Zi4v5jfp6NfyhDTMZLUnGl+DDYN7tmhZ51NMP/fo2E1GdPJe8IePHhQb731llwul2pra1seYRg6ffq0fD6fDh06pL59+7YuebmwBOZSdXV1GjBgwGWXvcydO1f9+vVrc2/WrFmaNWtWJ/1t0FVVVFSooqKizb0ff/wxQtmgKztx4oTy8vJ04sQJ7dy5U1dffXVrG++h0DEMQz5fotr/3GuRz9dbhmG0FgS7myt9D5mqBHGsIwAAANBWbW2tDMOQ0+nUr371q4D2zMxMPf3001qyZIkGDRqkPXv2BPSpqanR2LFjL/uspUuXaty4cZ2SN7qXYL/gf/LJJ/rZz34WoYzQFZ05c0b5+fk6ePCgtm/fruuvv75N+5AhQ3gPhYjFYpHN1qiWbzmCFZgM2WyN3bb4JF35e8jUEjyOdQQAAADaGjVqlNavX6/169drw4YNrdfIkSOVlpamDRs26IknnpAkFRYWatOmTa0zpSRp+/bt+uqrr1RUVBSpvwKAKOD3+1VUVKTq6mqtWbNG48ePD9qP91DoTJuWK6t1a9A2q3WLCgpuDXNGXUunrIWrr6/XqFGjJF3+WMfNmzd3xiMBAACALiEpKUkFBQUB95cuXSqLxaJp06a13nvhhRe0Zs0a3XHHHXr66afl9XpVVlamMWPG6LHHHgtj1gCizbx581RZWamCggIdO3ZMq1atatP+8MMPS+I9FEqlpc+oqqpQHo9xyUbkhqzWLcrOXqqSkrWRTjGirrgAxbGOAAAAQHD/vtTimmuu0UcffaR58+bp+eefV8+ePZWfn6+ysjI+HwO4Ip999pksFosqKytVWVkZ0H6hAMV7KHTsdrvc7rVasOA1bdy4RD5fb9lsp1RQkKuSkrWy2+2RTjGirqgAdSXHOjKwAQAAEM3+/Oc/B72fnZ3NqgAAna69d04wvIdCx263y+VaJJdL3XrD8VDocAEq1Mc6fl/zv4rrGd/m3oCMGzUgk83OAAAA8NM0fP2JGr5pe2LgOd/pCGUDAIglFJ/a6lABKtTHOkpS6vj71Dvpmo6kBwAAAEiSBmSOC/gC89TxH+TZtDRCGQEAEJtMF6DCcawjAAAAAABAV8Oyuo6zmunMsY4AAAAAACCWeL1eOZ0LlZExRamp9ysjY4qczoXyer2RTq1bMTUDimMdAQAAAABArPB6vcrJKZTHM09+/yJJFkmGysu3qqqqUG43p9v9VKYKUBzrCAAAAAAAYsX8+WXni095l9y1yO/Pk8djaMGC1+RyLYpUet2KqQIUxzoCAAAAAIBYUVm56/zMp0B+f542blwilyu8OXVXHToFDwCAsOjQ/o7mg4yOPEaSEWc+xpdoPr+zab3MP0hSj8GppmMSjl7VoWcZX9ebjkle7DYd4373OtMxkjTmwUmmY2Y+VGU6Zp9zmekYSSqdNdx0zHsVE03HDK343nSMJMX9Za/pmH4pQzr0rOZM82OwaXBPU/17NPlNPwMAEHsMw5DPl6j2P19a5PP1ZmPyn8jUJuQAAAAAAACxwGKxyGZrVPtfVxqy2RopPv1EFKAAAAAAAACCmDYtV1br1qBtVusWFRTcGuaMui8KUAAAAAAAAEGUlj6j7Owlslo36+JMKENW62ZlZy9VSUlxJNPrVihAAQAAAAAABGG32+V2r5XDUa309LuUknKf0tPvksNRLbd7rex2e6RT7DbYhBwAAAAAAKAddrtdLtciuVxiw/ErwAwoAAAAAACAn4DiU8dRgAIAAAAAAEBIUYACAAAAAAA4zzCMy3eCaRSgAAAAAABATPN6vXI6FyojY4pSU+9XRsYUOZ0L5fV6I51a1GATcgAAAAAAELO8Xq9ycgrl8cyT379IkkWSofLyraqqKuS0u07CDCgAAAAAABCz5s8vO198ylNL8UmSLPL78+TxzNWCBa9FMr2oQQEKAAAAAADErMrKXfL7pwZt8/vztHHjrjBnFJ1YggcAQIdP0zUf2JEtLY24DgRJ8iWaz+9sWq8OPavH4FTTMQlHrzIdY3xdbzpGkpIXu03HuN+9znTMmAcnmY6RpJkPVZmO2edcZjqmdNZw0zGS9F7FRNMxQyu+79Cz4v6y13RMv5Qhpvpbmo+afgYAIDoZhiGfL1Htf66zyOfrLcMwZLF0+EMjxAwoAAAAAAAQoywWi2y2RrX/NaEhm62R4lMnoAAFAAAAAABi1rRpubJatwZts1q3qKDg1jBnFJ0oQAEAAAAAgJhVWvqMsrOXyGrdrIszoQxZrZuVnb1UJSXFkUwvalCAAgAAAAAAMctut8vtXiuHo1rp6XcpJeU+paffJYejWm73Wtnt9kinGBXYhBwAAAAAAMQ0u90ul2uRXC6x4XiIMAMKAAAAAADgPIpPoUEBCgAAAAAAACFFAQoAAAAAAAAhRQEKAAAAAADgPMMwLt8JplGAAgAAAAAAMc3r9crpXKiMjClKTb1fGRlT5HQulNfrjXRqUYNT8AAAAAAAQMzyer3KySmUxzNPfv8iSRZJhsrLt6qqqlBu91rZ7fYIZ9n9MQMKAAAAAADErPnzy84Xn/LUUnySJIv8/jx5PHO1YMFrkUwvalCAAgAAAAAAMauycpf8/qlB2/z+PG3cuCvMGUUnluABABBOlst36aQgdWT7TCOuQ4+SL9F8jmfTepmO6TE41XSMJCUcvcp0jPF1vemY5MVu0zGS5H73OtMxYx6cZDpm5kNVpmMkaZ9zmemY0lnDO/Ss9yommo5Jq/jeXICV72ABAC0Mw5DPl6j2P29Z5PP1lmEYslg69pkMLfjpCwAAAAAAYpLFYpHN1qj2v7ozZLM1UnzqBBSgAAAAAABAzJo2LVdW69agbVbrFhUU3BrmjKITBSgAAAAAABCzSkufUXb2Elmtm3VxJpQhq3WzsrOXqqSkOJLpRQ0KUAAAAAAAIGbZ7Xa53WvlcFQrPf0upaTcp/T0u+RwVMvtXiu73R7pFKMCm5ADAAAAAICYZrfb5XItksslNhwPEWZAAQAAAAAAnEfxKTQoQAEAAAAAACCkKEABAAAAAACcZxjG5TvBNApQAAAAAAAgpnm9XjmdC5WRMUWpqfcrI2OKnM6F8nq9kU4tarAJOQAAAAAAiFler1c5OYXyeObJ718kySLJUHn5VlVVFXISXidhBhQAAAAAAIhZ8+eXnS8+5aml+CRJFvn9efJ45mrBgtcimV7UoAAFAAAAAABiVmXlLvn9U4O2+f152rhxV5gzik4swQMAIFp16AThjh073JGtOo048zG+xI7ldzatl+mYHoNTTcckHL3KdIwkGV/Xm45JXuw2HeN+9zrTMZI05sFJpmNmPlTVoWftcy4zHVP60HBT/Q9/8aPcD5p+DAAgChmGIZ8vUe1/BrLI5+stwzBksXTscwhaMAMKAAAAAADEJIvFIputUe1/nWbIZmuk+NQJKEABAAAAAICYNW1arqzWrUHbrNYtKii4NcwZRScKUAAAAAAAIGaVlj6j7Owlslo36+JMKENW62ZlZy9VSUlxJNOLGhSgAAAAAABAzLLb7XK718rhqFZ6+l1KSblP6el3yeGoltu9Vna7PdIpRgU2IQcAAAAAADHNbrfL5Vokl0tsOB4izIACAAAArtBHH30kq9UacMXFxammpqZN3/379ysvL092u11JSUmaPXu2jh07FqHMAUSLPXv2yOFwaNSoUerTp4/S0tI0c+ZMHThwoE2/xx9/POj7asSIERHKvOuh+BQa3WoGVMPXn2hA5rhIp4EuhnGBYBgXCIZxgX93/Ju9Ssq4MdJpIIrMmTNHN910U5t7WVlZrX+ura3Vbbfdpv79+2vx4sXyer169dVX9fnnn6umpkY9enSrj+cAupBXXnlFu3fv1owZMzR69GgdOXJEb775psaNG6fq6uo2Bab4+Hi9/fbbMoyLJ7/169cvEmkjhnSrn3AN3+zlFwcEYFwgGMYFgmFc4N81fPspBSh0qltvvVUPPPBAu+2lpaVqamrSp59+qpSUFEnSzTffrDvvvFPLly/Xk08+Ga5UAUSZ4uJiVVRUtClkFxUV6YYbbtDixYu1YsWK1vs9evTQrFmzIpFmt8ASvNBgCR4AAADQiU6ePKlz584FbVu3bp3y8/Nbi0+SNHnyZA0bNkyrV68OV4oAotCECRMCZlFmZWVp5MiR8ng8Af39fr+8Xm+40uvyvF6vnM6FysiYotTU+5WRMUVO50L+P+pEFKAAAACATvL444+rb9++io+P16RJk/TXv/61te3w4cM6evRowBI9SRo/frz27t0bzlQBxIj6+noNHDiwzb1Tp06pb9++6tevn5KSkuRwONTY2BihDCPP6/UqJ6dQ5eU5+vbbP6m29n/17bd/Unl5jnJyCilCdZJutQQPAAAA6Ip69uyp6dOn65577tHAgQP1xRdfqKysTLfffrt2796tMWPGqK6uTpKUnJwcEJ+cnKyGhgb5fD7ZbLZwpw8gSq1cuVK1tbUqKSlpvTdkyBA9++yzGjdunPx+v7Zs2aLf/va32rdvnz788ENZrbE3T2X+/DJ5PPPk9+ddctcivz9PHo+hBQtek8u1KFLpRY0uV4Bqampq+d9/1Qe0nWs+rVPHfwh3SujiGBcIhnGBYBgXIWRcvkunBHXoOZLFHzzwrK9Jje2Mibgz5h929uRZ0zGS1KP5uPlnGf80/5wzPU3HSFLTEfP7YBz+4scOPeuTfqfNP+tf5p517JuTki5+7uwMOTk5ysnJaf3n/Px8FRYWavTo0Xr++ef1wQcftD6vV69eAfHx8fGtOQUrQF2IDbaMJlpcOKjr88+lhobI5tJdXBgPnTmWET32798vh8Oh3NxczZ49u/V+aWlpm35FRUW67rrrtGDBAq1Zs0ZFRUVB/33R/B5as2az/P4CSZ8EtPn9g/X++5v1858XhD+xbsDUe8joYlauXGmo5eMlFxcXFxcXFxcXV8iulStXhvyz7axZs4z4+HjD7/cbe/bsMSwWS9DnPvvss4bVajWam5uD/nv4jMz1n65wjGV0L0eOHDEyMzON9PR0o66u7rL9m5qajLi4OOOpp55qtw/vIa7/dP2U91CXmwE1depUrVy5Uunp6UpISIh0OgAAAIgyTU1N+vbbbzV16tSQPys1NVXNzc1qbGxsXXp3YSneperq6jRgwIB2l9/xGRnBhHMso/s4ceKE8vLydOLECe3cuVNXX331ZWPi4+OVlJSkhv8w/ZD3EIIx8x6yGIZhhCEnAAAAIOZMnz5dmzdvbt3c96qrrtLEiRP17rvvtuk3fPhwpaam6k9/+lMk0gQQJc6cOaM777xTe/fu1fbt2zV+/PifFHfy5En169dPv/jFL7Rs2bIQZ4lYFXu7iwEAAACd7NixYwH3PvvsM1VWVrb5VriwsFCbNm1SbW1t673t27frq6++anffFQD4Kfx+v4qKilRdXa01a9YELT6dOXNGJ0+eDLj/3//935Kku+++O+R5InYxAwoAAAC4QpMnT1ZCQoJuueUWDR48WH//+9/11ltvqVevXtq9e7euv/56SdIPP/ygcePGqV+/fnr66afl9XpVVlamoUOHqqamhhPwAHTYnDlz9MYbb6igoEAzZswIaH/44Yd16NAh3XjjjZo1a5aGDx8uSdqyZYs2b96se+65R5s2bQp32oghFKAAAACAK/Sb3/xGq1at0sGDB3XixAkNGjRIU6ZM0YsvvqjMzMw2fT0ej+bNm6edO3eqZ8+eys/PV1lZmQYNGhSh7AFEg4kTJ2rHjh3ttp87d04//vijnE6nPv74Yx0+fFjnzp1TVlaWHnnkERUXFysuLi6MGSPWUIACAAAAAABASLEHFAAAAAAAAEKqyxegmpub9dxzzyklJUW9e/fWhAkTtG3btkinhTBpbGzUwoULdffddyspKUlWq1UrVqwI2nf//v3Ky8uT3W5XUlKSZs+eHXRDUHR/e/bskcPh0KhRo9SnTx+lpaVp5syZOnDgQEBfxkVs+OKLL1RUVKRrr71WiYmJSkpK0i233KJVq1YF9GVMxK7S0lJZrVaNHj06oI1xAQAAEFo9Ip3A5fz85z/XunXrNHfuXGVlZWn58uW655579OGHH+qWW26JdHoIsWPHjumll15SWlqaxo4dqw8//DBov9raWt12223q37+/Fi9eLK/Xq1dffVWff/65ampq1KNHlx/qMOGVV17R7t27NWPGDI0ePVpHjhzRm2++qXHjxqm6ulojRoyQxLiIJYcOHdLJkyf12GOPaciQITp16pTWrl2rRx99VIcOHdILL7wgiTERy2pra/Xyyy+rT58+QdsYFwAAACFmdGHV1dWGxWIxlixZ0nrv9OnTRlZWlpGbmxvBzBAuzc3NRn19vWEYhrFnzx7DYrEY77zzTkC/X/7yl0ZiYqLxww8/tN7btm2bYbFYjLfeeits+SI83G634fP52tw7cOCAER8fbzz66KOt9xgXsc3v9xtjx4410tLSWu8xJmLXzJkzjSlTphh33HGHccMNN7RpY1wAAACEXpdegrdmzRr16NFDTz31VOu9Xr166YknnpDb7VZtbW0Es0M42Gw2DR48+LL91q1bp/z8fKWkpLTemzx5soYNG6bVq1eHMkVEwIQJEwJmJGRlZWnkyJHyeDyt9xgXsc1isSg1NbXNWGFMxKYdO3Zo3bp1ev3114O2My4AAABCr0sXoD799FMNGzYsYLr8+PHjW9uBw4cP6+jRo7rpppsC2saPH6+9e/dGICtEQn19vQYOHCiJcRGrTp06pePHj+vrr7/W0qVLtXXrVj333HOSGBOxyu/3y+l06qmnntLIkSMD2hkXAAAA4dGlNzWoq6tTcnJywP3k5GQZhqHDhw9HICt0NXV1dZLU7lhpaGiQz+eTzWYLd2oIo5UrV6q2tlYlJSWSGBexqri4WL///e8ltcygdLlcrbNoGROxadmyZfruu+9UVVUVtJ1xAQAAEB5degZUU1OTevXqFXA/Pj6+tR24MA4YK7Fr//79cjgcys3N1ezZsyUxLmLV3LlztW3bNq1YsUKTJ0+Ww+FoPTmTMRF7GhoatHDhQr344osaMGBA0D6MCwAAgPDo0jOgEhISdObMmYD7p0+fbm0HLowDxkpsqq+v17333qv+/fvr/fffl8VikcS4iFXDhg3TsGHDJEmPPPKIpk6dqjlz5qioqIgxEYPmz5+vpKQkORyOdvswLgAAAMKjSxegkpOTgy6zuzBdfsiQIeFOCV3QhWUTF8bFperq6jRgwACWTkSpEydOKC8vTydOnNDOnTt19dVXt7YxLiBJ06dP17Zt27R//37GRIw5ePCg3nrrLblcrtZDSwzD0OnTp+Xz+XTo0CH17duXcQEAABAmXXoJ3tixY/XVV1/p5MmTbe5//PHHslgsGjt2bIQyQ1cyZMgQDRo0SHv27Aloq6mpYZxEqTNnzig/P18HDx7UH//4R11//fVt2hkXkC4unbJarYyJGFNbWyvDMOR0OpWRkaGMjAxlZmaqurpaX375pTIzM/XSSy8xLgAAAMKkSxegpk+frrNnz+oPf/hD673m5mYtX75cEyZMaHNcMmJbYWGhNm3a1PottyRt375dX331lYqKiiKYGULB7/erqKhI1dXVWrNmTevJmP+OcRE7/vGPfwTcO3v2rN555x0NGDCg9fQzxkTsGDVqlNavX6/169drw4YNrdfIkSOVlpamDRs26IknnpDEuAAAAAgHi2EYRqST+E9mzpypDRs2aM6cOcrKytLy5cu1Z88eVVVVKTc3N9LpIQzKy8v1r3/9S7W1tfrdzuCxXQAAAa9JREFU736nBx54QDfeeKMkyel0ym6364cfftC4cePUr18/Pf300/J6vSorK9PQoUNVU1PD8okoM2fOHL3xxhsqKCjQjBkzAtoffvhhSWJcxJAHHnhAJ06c0O23366UlBQdOXJEq1at0pdffqnly5fr0UcflcSYgDRx4kQdP35c+/bta73HuAAAAAi9Ll+Aam5u1q9//WutXLlS//znPzV69GiVlJRoypQpkU4NYZKRkaHvvvsuaNs333yjoUOHSpI8Ho/mzZunnTt3qmfPnsrPz1dZWZkGDRoUznQRBhMnTtSOHTvabT937lzrnxkXsWH16tV6++239be//U3Hjx9X3759NX78eBUXF2vSpElt+jImYtvEiRPV0NCgzz77rM19xgUAAEBodfkCFAAAAAAAALq3Lr0HFAAAAAAAALo/ClAAAAAAAAAIKQpQAAAAAAAACCkKUAAAAAAAAAgpClAAAAAAAAAIKQpQAAAAAAAACCkKUAAAAAAAAAgpClAAAAAAAAAIKQpQAAAAAAAACCkKUAAAAAAAAAgpClAAAAAAAAAIKQpQAAAAAAAACKn/B7iT3wL5/8s3AAAAAElFTkSuQmCC",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326c88cc0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PyCall\n",
    "@pyimport matplotlib.gridspec as gridspec\n",
    "\n",
    "fig = figure(figsize=(12, 4))\n",
    "\n",
    "gs = gridspec.GridSpec(1, 4,width_ratios=[10, 2, 1, 2])\n",
    "\n",
    "ax0 = subplot(get(gs, (0)))\n",
    "ax0[:imshow](G, cmap=\"viridis\", interpolation=\"none\", aspect=\"auto\")\n",
    "ax0[:text](42, 12, \"G\", color=\"w\", size=20)\n",
    "\n",
    "y = collect(1:50)\n",
    "\n",
    "ax1 = subplot(get(gs, (1)))\n",
    "ax1[:plot](m, y)\n",
    "ax1[:text](-0.07, 25, \"m\", color=\"k\", size=20)\n",
    "ax1[:set_xticks]([])\n",
    "ax1[:invert_yaxis]()\n",
    "\n",
    "ax2 = subplot(get(gs, (2)))\n",
    "ax2[:set_frame_on](false)\n",
    "ax2[:set_xticks]([])\n",
    "ax2[:set_yticks]([])\n",
    "ax2[:text](0.5, 0.5, \"=\", color=\"k\", size=20)\n",
    "\n",
    "y = collect(1:25)\n",
    "\n",
    "ax3 = subplot(get(gs, (3)))\n",
    "ax3[:plot](d, y, \"o\")\n",
    "ax3[:text](-0.05, 12, \"d\", color=\"k\", size=20)\n",
    "ax3[:set_xticks]([])\n",
    "ax3[:invert_yaxis]()\n",
    "\n",
    "fig[:tight_layout]()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Noise free: minimum norm\n",
    "\n",
    "As in the other notebooks, we're implementing the 'least' or 'minimum' norm, a unique solution among the inifinity of least squares solutions to this underdetermined problem. \n",
    "\n",
    "Estimate the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m_est = G' * inv(G * G') * d;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then uses it to predict the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d_pred = G * m_est;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And plot everything to make sure it looks OK."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326e26b70>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(m, d, m_est, d_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Direct general solver\n",
    "\n",
    "We can use Julia's linalg [backlash operator](http://docs.julialang.org/en/release-0.5/stdlib/linalg/#Base.\\) to solve the system. The operation `A \\ B = x` is such that `A*x == B` when `A` is square, and when it's not square, it implements a solution via factorization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m_est = G \\ d \n",
    "d_pred = G * m_est;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326ce3748>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_all(m, d, m_est, d_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## QR factorization\n",
    "\n",
    "As always, this only works if **G** is square."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.LinAlg.QRCompactWY{Float64,Array{Float64,2}}([-1.11763 -0.923579 … -4.75542e-46 -4.09877e-48; 0.066959 -0.650178 … -1.2878e-43 -1.33141e-45; … ; 0.0 0.0 … -0.142587 0.318841; 0.0 0.0 … 1.00002 0.727125],[1.89475 -0.279441 … -1.22382e-42 0.0; 5.92879e-323 1.94842 … -2.47568e-43 0.0; … ; 2.78134e-309 NaN … 2.0 0.0; 6.92746e-310 0.0 … 3.50639e151 0.0])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F = qrfact(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3275c8978>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(F[:Q], cmap=\"viridis\", interpolation=\"none\")\n",
    "show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = F[:Q]' * d\n",
    "m_est = inv(F[:R]) * p\n",
    "d_pred = G * m_est\n",
    "plot_all(m, d, m_est, d_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## LU Factorization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Base.LinAlg.LU{Float64,Array{Float64,2}}([1.0 0.727177 … 0.0 0.0; 0.141794 0.624068 … 0.0 0.0; … ; 0.0 0.0 … 0.14275 -0.318723; 0.0 0.0 … 1.00002 0.727125],[1,2,3,4,6,6,7,8,9,10  …  16,17,18,19,20,21,22,23,24,25],0)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "F = lufact(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x3268f7940>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "imshow(F[:L]*F[:U], cmap=\"viridis\", interpolation=\"none\")\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I don't think there's a method that will work for this non-square matrix, but Julia exposes [a lot of BLAS functions](http://docs.julialang.org/en/release-0.5/stdlib/linalg/#module-Base.LinAlg.BLAS). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using regression methods\n",
    "\n",
    "We'll use [ridge regression](http://multivariatestatsjl.readthedocs.io/en/latest/lreg.html#ridge-regression), also known as Tikhonov regularization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using MultivariateStats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x326e26ba8>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m_est = ridge(G, d, 1);\n",
    "d_pred = G * m_est[1:end-1];\n",
    "plot_all(m, d, m_est, d_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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